FIRST   OBSERVATIONS 

IN 

ASTRONOMY 


A  HANDBOOK  FOR  SCHOOLS  AND  COLLEGES 


BY 


MARY  E.  BYRD,  PH.  D. 

Former  Director  of  Smith  College  Observatory 
Teacher  of  Astronomy  in  the  Normal  College  of  the  City  of  New  York 


CONCORD,  N.  H. 

THE  RUMFORD  PRESS 

1913 


COPYRIGHT,  1914 
BT  MARY  E.  BYRD 


PREFACE 

REAL  knowledge  in  science  depends  upon  direct  study  of  objects 
and  phenomena.  Astronomy  is  no  exception.  Literally  to  look 
up,  to  see  with  our  own  eyes  and  to  find  out  by  seeing, —  these 
things  are  the  beginnings  of  astronomy. 

As  a  guide  to  first  observations,  this  handbook  has  been  written. 
With  few  exceptions,  the  mechanical  appliances  required  can 
be  made  by  a  carpenter  or  by  the  students  themselves.  Simple 
tools  are  best  at  first.  It  needs  but  slight  experience  with 
protractors,  plumb  lines,  gnomons,  and  sun-dials  to  realize  how 
aptly  they  can  be  used  in  scientific  training,  and  how  much  mean- 
ing they  put  into  different  subjects.  Not  a  little  light  will  reach 
some  of  the  dark  places  of  geography  and  arithmetic,  when  teach- 
ers are  accustomed  to  make  simple  observations,  and  know  how 
to  interest  boys  and  girls  in  finding  the  latitude  of  the  school 
building  with  the  window  gnomon,  and  the  error  of  the  clock  from 
the  horizontal  sun-dial.  At  present,  we  sometimes  have  so-called 
courses  of  nature  study  with  the  sun  in  heaven  left  out! 

A  few  topics  of  advanced  character,  dealing  mainly  with  time 
and  longitude,  have  been  included  in  the  final  chapter;  but,  as  a 
rule,  simplicity  of  treatment  has  been  carefully  guarded,  and 
mathematical  knowledge  beyond  elementary  branches  is  not 
required. 

No  effort  has  been  made  to  deal  even  in  a  cursory  manner  with 
descriptive  astronomy.  It  must,  of  course,  receive  its  due  meed 
of  attention,  and  when  the  sky  is  cloudy,  or  the  weather  very  cold, 
emphasis  is  naturally  placed  on  that  part  of  the  subject. 

To  add  vividness  to  the  illustrations,  many  observations  have 
been  prepared,  under  the  writer's  direction,  in  different  parts 
of  the  country,  by  different  students,  and  are  marked  with  their 
initials. 

Grateful  acknowledgement  is  made  to  those  who  have  read 
the  book  wholly  or  partly  in  manuscript  and  given  help  in  other 

283488 


iv  PREFACE 

ways,  especially  to  Professor  Harriet  W.  Bigelow  of  Smith  Col- 
lege and  Mary  M.  Hopkins,  Instructor  there,  to  Professor  Anne  S. 
Young  of  Mount  Holyoke  and  Professor  Ellen  Hayes  of  Wellesley. 
Mention  should  also  be  made  of  Louise  Barber,  and  Jane  T. 
Vermilye,  former  assistants  at  Smith,  who  have  contributed  some 
of  the  more  difficult  observations,  and  to  another  Smith  alumna, 
Lucy  Stoddard,  who  has  aided  in  preparing  the  index. 

Professor  William  F.  Rigge  has  kindly  allowed  the  use  of  two 
diagrams,  illustrating  a  solar  eclipse,  which  accompanied  an  arti- 
cle of  his  in  Popular  Astronomy.  In  this  permission  the  editor 
of  the  journal,  Doctor  Herbert  C.  Wilson,  courteously  joins, 
and  also  gives  leave  to  make  use  here  of  articles  by  the  writer 
which  first  appeared  in  the  same  journal. 

Freedom  of  access  to  the  library  and  the  use  of  some  of  the 
astronomical  instruments  of  the  State  University  of  Kansas  are 
privileges  that  have  been  highly  appreciated;  and  no  small  debt 
is  owed  to  A.  Marks,  a  jeweler  of  Lawrence,  Kansas,  whose  kind- 
ness and  courtesy  in  sending  accurate  time  by  telephone  rendered 
it  possible  to  test  a  home-made  transit  instrument,  and  to  de- 
termine longitude  from  local  observations. 

References  to  descriptive  astronomy  are  made  to  "  Young's 
Elements  of  Astronomy,"  and  are  designated  by  "  Young." 
Those  to  "Byrd"  refer  to  the  writer's  "  Laboratory  Manual  in 
Astronomy." 

MARY  E.  BYRD. 

NEW  YORK,  N.  Y. 
November,  1913. 


CONTENTS. 

PAGE 

INTRODUCTION YII-XI 

CHAPTER  I.  Observing  station  and  laboratory;  Plumb  lines;  Merid- 
ian line;  Home-made  instruments;  Miscellaneous  appliances; 
Definitions;  Directions  for  observing  and  recording 1-15 

CHAPTER  II.  Points  in  sun's  diurnal  path ;  Constellations  identified ; 
Star-maps;  Different  kinds  of  time;  Standard  meridians  and 
time  sections;  Almanacs;  Celestial  globe;  Latitude  and  decli- 
nation of  zenith;  Checks  for  altitude  and  azimuth 16-26 

CHAPTER  III.  Sun's  diurnal  path,  with  altazimuth,  with  solar-image 
gnomon;  Planets  identified;  Constellations  mapped;  American 
Ephemeris;  Changing  from  one  kind  of  time  to  another;  Plotting 
on  star-maps;  Orienting  celestial  globe 27-45 

CHAPTER  IV.  Sun's  apparent  motion  among  the  stars;  Sun's  noon 
altitude  and  latitude  of  place;  First  observations  of  the  moon; 
Moon's  synodic  period;  Greenwich  time;  Sidereal  time;  Inter- 
polating; Plotting  on  celestial  globe;  First  tests  for  opera-glasses; 
Preliminary  study  of  the  telescope 46-62 

CHAPTER  V.  First  observations  with  opera-glasses;  Lunar  paths; 
Moon's  rate  of  motion  and  sidereal  period;  Planets  mapped 
among  the  stars;  Conjunction  of  planets;  Time  from  gnomon, 
from  transit  of  sun  or  star;  Sidereal  day  from  star  transits; 
Sidereal  and  mean  solar  time;  Times  of  lunar  phases  and  eclipses; 
Field  of  view  and  magnifying  power  of  opera-glasses;  Focal 
length  and  field  of  view  of  small  telescope 63-80 

CHAPTER  VI.  First  observations  with  telescope;  Lunar  eclipses; 
Shooting  stars;  Comets;  Color,  brightness,  and  motion  of  stars; 
Position  of  equator,  ecliptic  and  Milky  Way;  Stars  and  nebulae 
with  opera-glasses;  Latitude  from  altitude  of  stars;  Time  from 
the  sun-dial;  Charting  diurnal  paths;  Magnifying  power  and 
proficiency  of  telescope 81-99 

CHAPTER  VII.  Partial  solar  eclipse;  Paths  of  planets  among  the 
stars;  Planets,  nebulae,  and  stars  with  small  telescope;  General 
problem  of  time  with  transit  instrument;  Time  with  home-made 
transit  instrument;  Latitude  and  longitude  without  observation; 
Longitude  from  time  determinations 100-119 

APPENDIX,  Latitudes  and  Longitudes  of  Places 120 

INDEX 121-126 


INTRODUCTION. 


i.  Equipment. — The  unaided  eye  is  no  mean  astronomical 
instrument,  and  when  the  sky  is  clear,  the  main  objects  of  astro- 
nomical study  are  ready  at  hand.  There  is,  however,  little  value 
in  haphazard  star-gazing.  A  definite  scheme  of  work,  under 
competent  instruction,  should  be  carried  on  regularly,  in  the  day- 
time and  in  the  evening.  Mechanical  appliances  at  first  may 
be  few  and  simple,  as  for  example: 

1.  Meridian  stone  and  carpenter's  level. 

2.  Altazimuth  for  measuring  angles. 

3.  Plumb  lines  and  sun-dial  for  finding  time. 

4.  Gnomon  for  determining  latitude  and  time. 

5.  Celestial  globe  and  good  watch  or  clock. 

6.  Opera-glasses  or  small  telescope.* 

This,  in  the  main,  is  the  equipment  assumed  in  giving  instruc- 
tions for  a  large  number  of  observations.  Details  regarding  it 
are  to  be  found  in  the  first  chapter,  and  there  also  other  apparatus 
is  described. 

The  suggestion  may  seem  premature,  but  it  is  certain  that  a 
small  building  devoted  to  astronomy  is  an  advantage  in  many 
ways.  It  affords  the  needed  shelter  for  plumb  lines,  and  gives 
opportunity  for  mounting  permanently  instruments  like  the  sun- 
dial and  home-made  transit  which  must  be  critically  adjusted 
in  the  meridian.  A  good  view  of  the  heavens  should  be  insured 
from  its  roof,  and  if  a  section  of  that  is  removable,  work  with 
small  telescopes  is  facilitated.  Wear  and  tear  is  also  saved  by 

*With  the  exception  of  a  good  time-piece  and  the  celestial  globe  which  many 
schools  possess,  the  cost  of  these  appliances  will  probably  amount  to  about 
fifty  dollars. 

vii 


INTRODUCTION 

not  carrying  instruments  from  place  to  place,  and  efficiency  and 
rapidity  in  observing,  promoted. 

2.  Fundamental  observations. — It  has  been  the  aim  in  the 
following  chapters  to  present  a  large  number  of  observations, 
extending  over  a  somewhat  wide  range  of  topics,  and  including 
those  that  are  short  and  simple,  as  well  as  those  requiring  not  a 
little  time  and  effort.  From  them,  if  desired,  different  grouping* 
can  be  made,  and  courses  adapted  to  varying  needs  and  condi- 
tions. In  any  scheme,  as  far  as  practicable,  place  should  be 
given  to  the  essential  observations  along  different  lines.  Thus, 
in  all  direct  study  of  the  heavens,  five  subjects  stand  out  promi- 
nently: 

1.  The  Constellations. 

2.  Diurnal  Paths  of  Heavenly  Bodies. 

3.  Paths  of  Sun,  Moon,  and  Planets  among  the  Stars, 

4.  Face  Appearance  of  Sun  and  Moon. 

5.  Latitude  and  Time  from  Sun  and  Stars. 

The  following  list  of  observations  is  suggested  as  giving  due 
recognition  to  each  of  the  above  subjects,  and  providing  a  mid- 
way course  for  beginners,  neither  very  easy  nor  very  hard: 

1.  Become  familiar  with  thirty-five  constellations  so  as  to 
recognize  them  readily  in  different  seasons. 

2.  Make  separate  sketches  of  twenty  constellations,  directly 
from  the  sky,  including  at  least  seven  stars  in  each. 

3.  Twice  in  the  same  evening,  allowing  an  interval  of  an  hour 
or  more,  note  the  position  of  three  bright  constellations,  one 
chosen  near  the  eastern  horizon,  one  near  the  meridian,  and  the 
third  near  the  horizon  toward  the  west. 

4.  Orient  four  of  the  circumpolar  constellations  in  reference 
to  the  North  Star,  twice  in  the  same  evening,  allowing  an  interval 
of  an  hour  or  more. 

5.  Fix  a  diurnal  path  of  the  sun  by  finding  its  altitude  and 
azimuth  at  five  different  times,  including  if  possible  southing 
and  setting. 

viii 


INTRODUCTION 

6.  At  intervals  of  three  weeks  or  more,  fix  approximately  five 
other  diurnal  paths  of  the  sun,  making  several  determinations 
of  altitude  and  azimuth. 

7.  Fix  a  diurnal  path  of  the  moon  by  measuring  its  altitude  and 
azimuth  at  five  different  times,  including  either  rising,  southing 
or  setting. 

8.  Check  meridian  altitudes  from  declination,  and  azimuths 
at  rising  or  setting  from  the  celestial  globe. 

9.  Plot  all  diurnal  paths  on  rectangular  paper  and  note  the 
following  points : 

(1)  Changes  in  noon  altitude  and  sunset  point. 

(2)  Connection  between  the  extent  of  solar  paths  and  seasons 
of  the  year. 

(3)  Likeness  or  unlikeness  of  solar  and  lunar  paths. 

(4)  Connection  between  the  extent  of  a  path  and  declination 
of  the  body. 

10.  Note,  two  or  three  times,  at  an  interval  of  a  month  or 
more,  the  zodiacal  constellation  first  seen  in  the  west  after  sunset. 

11.  Find  out  by  observation  how  soon  the  moon  is  visible 
after  new  moon,  where  it  is  first  seen,  and  in  what  direction  the 
horns  point. 

12.  Find  when  and  where  the  moon  rises  on  a  night  when  it 
is  full,  both  in  the  fall  and  in  the  spring. 

13.  A  day  or  two  before  full  moon,  and  a  day  or  two  after, 
note  which  limb  is  defective. 

14.  On  five  or  more  nights  in  one  lunation,  fix  the  moon's 
place  by  estimating  its  distance  and  angular  direction  from 
neighboring  stars. 

15.  From  the  data  of  the  preceding  observation,  find  the  moon's 
sidereal  period,  and  its  daily  rate  of  motion. 

16.  From  observations  of  the  phase  of  the  moon,  made  in 
two  or  three  lunations,  find  the  approximate  length  of  its  synodic 
period. 

17.  Map  one  of  the  bright  planets  among  the  stars,  on  ten 
evenings  at  intervals  of  a  few  days  or  a  week  or  two,  according 
to  its  rate  of  motion. 

ix 


INTRODUCTION 

18.  In  like  manner,  map  a  second  bright  planet  on  five  even- 
ings. 

19.  From  the  data  obtained  by  observations  17  and  18  plot 
the  paths  of  the  planets  observed,  on  specially  prepared  star- 
maps,  and  note  the  following  points: 

(1)  In  what  direction  each  planet  is  moving  among  the  stars, 
and  whether  the  direction  of  either  changes. 

(2)  How  rates  of  motion  of  one  planet  at  different  times,  or 
both  planets  at  the  same  time,  compare. 

(3)  How  the  paths  are  placed  with  regard  to  the  ecliptic,  and 
what  constellations  are  traversed  in  whole  or  in  part. 

20.  Plot  on  the  celestial  globe  the  positions  of  a  planet  for  two 
dates,  and  find  its  motion  in  right  ascension  and  declination  for 
the  interval. 

21.  Locate  a  north  and  south  line  with  the  aid  of  a  gnomon. 

22.  Observe  the  transit  of  the  same  star  twice  over  the  same 
reference  line,  so  as  to  find  out  which  is  the  longer,  the  sidereal 
or  mean  solar  day,  and  by  how  many  minutes  the  two  differ. 

23.  At  sun  noon  find  the  error  of  a  watch  within  a  minute, 

(1)  From  the  gnomon. 

(2)  From  plumb  lines  used  as  a  transit  instrument. 

24.  At  any  hour  of  the  day,  find  the  error  of  a  watch  within 
a  minute  from  the  sun-dial. 

25.  Determine  the  latitude  of  the  place  of  observation  within 
half  a  degree, 

(1)  From  the  sun's  altitude  at  noon. 

(2)  From  the  altitude  of  a  star  south  of  the  zenith. 

(3)  From  the  altitude  of  the  North  Star,  on  or  off  the  meridian. 

26.  Trace  the  celestial  equator  and  ecliptic  in  the  heavens  by 
the  stars  near  their  paths,  noting  the  position  of  the  equinoxes. 

27.  Make  two  sketches  five  or  six  months  apart,  showing  where 
the  equator  and  ecliptic  intersect  the  horizon. 

28.  Determine  the  magnifying  power  of  an  opera-glass,  and 
test  it  for  double  field  of  view,  double  image,  and  fringes  of  light. 

29.  Examine  ten  objects  with  opera-glasses,  including  sun, 
planets,  star  clusters,  nebulae,  and  double  stars. 


INTRODUCTION 

30.  Identify  seven  objects  on  the  moon. 

31.  Determine  the  focal  length,  field  of  view,  and  magnifying 
power  of  a  small  telescope. 

32.  Examine  with  a  telescope  ten  objects,  including  sun,  plan- 
ets, star  clusters,  nebulae,  and  double  stars. 

33.  Identify  fifteen  objects  on  the  moon. 

To  carry  through  observations  like  these  intelligently,  and 
derive  satisfactory  results  really  requires  more  and  means  more 
than  is  easily  realized  by  merely  reading  them  over.  One  of  the 
objects  in  writing  the  handbook  has  been  to  present  in  orderly 
sequence  the  precepts,  explanations,  and  illustrative  observa- 
tions that  are  needed  in  actually  doing  the  work  which  is  here 
briefly  indicated. 


XI 


CHAPTER  I. 

PLACE  FOR  OBSERVING;  HOME-MADE  INSTRUMENTS;  MISCELLANEOUS  APPLI- 
ANCES; DEFINITIONS;  DIRECTIONS  FOR  OBSERVING  AND  RECORDING. 

3.  Observing  station  and  laboratory. — The  first  requisite  for 
an  observing  station  is  a  good  view  of  the  heavens.     The  horizon 
line  on  the  south,  and  either  on  the  west  or  east  should  be,  as 
far  as  possible,  unobstructed  by  trees  and  buildings.     If  there 
is  no  store-room  near  at  hand,  water-tight  lockers  should  be 
provided,  in  order  to  protect  instrumental  appliances  from  the 
weather,  when  not  in  use. 

There  are  advantages  in  an  observing  station  on  the  ground; 
but,  since  the  all-important  thing  is  to  see  the  sky,  it  may  be 
necessary  to  provide  for  it  on  a  flat  roof.  Wherever  placed,  it 
should  open  directly  upon,  or  closely  adjoin,  one  or  more  well- 
lighted  rooms,  for  really  efficient  observing  depends  intimately 
upon  work  at  the  desk.  This  laboratory,  if  the  term  may  be 
allowed,  is  the  place  for  consulting  almanacs,  maps,  and  globes 
during  observation,  for  making  sketches,  and  writing  the  notes 
of  the  evening's  work.  Here,  in  the  daytime,  instruments  are 
examined  and  tested,  preparatory  to  their  use,  and  the  different 
operations  carried  on  which  are  required  in  reducing  and  dis- 
cussing observations. 

4.  Meridian  stone. — When  routine  observing  is  done  on  the 
ground,  set  a  flagstone,  about  three  by  five  feet,  where  the  best 
view  of  the  celestial  meridian  is  obtained  (§  15,  20}.     Let  it  be 
carefully  levelled,  and  rest  on  a  sand  foundation,  a  foot  or  two 
deep,  that  it  may  be,  as  little  as  possible,  disturbed  by  the  weather. 

On  the  roof,  a  wooden  platform  somewhat  larger  takes  the 
place  of  the  stone.  It  should  be  painted  and  well  braced  to 

1 


OBSERVATIONS  IN  ASTRONOMY 

prevent  warping  and  shift  in  position,  which  would  be  likely  to 
vitiate  the  level  and  displace  the  meridian  line. 

If,  as  often  happens,  it  is  desirable  to  accommodate  more  than 
one  observer  at  the  same  time,  there  may  be  several  stones  or 
platforms  with  the  meridian  line  (§6)  marked  on  each. 

5.  Gnomon. — An  upright  shaft  set  firmly  in  place  on  a  hori- 
zontal  surface   constitutes  the   common   gnomon.     Instead   of 
the  upright,  the  section  of  a  sheltered  plumb  line  may  be  employed 
(§  43,  Obs.  2),  but  neither  shaft  nor  shadow  is  essential.     Almost 
any  window,  facing  in  a  southerly  direction,  can  be  utilized  for  a 
gnomon  in  which  the  sun's  image  takes  the  place  of  the  shadow. 

The  essentials  are  few  and  simple.  Let  the  lower  sash  contain 
a  single,  large  pane  of  plate  glass,  and  a  projecting  board  be 
placed  at  right  angles  to  it.  The  latter  should  be  covered  with 
white  paper  or  cardboard,  and  a  piece  of  dark  paper  with  a  small, 
nearly  circular  aperture  pasted  on  the  glass.  The  height  of  the 
gnomon  is,  then,  the  perpendicular  from  the  center  of  the  aperture 
to  the  projecting  board,  and  the  length  of  the  "shadow"  is  the 
distance  from  the  foot  of  this  perpendicular  to  the  center  of  the 
solar  image  which  is  formed  on  the  board  by  light  passing  through 
the  aperture  (§31). 

This  solar-image  gnomon  is  especially  convenient  in  cold  wea- 
ther, and  at  all  times  the  required  measurements  are  made  with 
marked  accuracy  and  rapidity.  It  may  be  adapted,  if  desired, 
for  use  out  of  doors,  by  substituting  for  the  upright  post  a  straight 
edge  having  a  long,  narrow  slot,  and  movable  disk  with  a  circular 
aperture. 

6.  Meridian  line. — A  meridian  line  is  essential  in  using  much 
of  the  simple  apparatus  required  in  elementary  astronomy.     It 
may  be  located  approximately  by  the  North  Star,  or  from  the 
shadow  of  a  common  gnomon  (§  61);  but  it  is  more  accurately 
determined  by  an  image  of  the  sun  (§5). 

First,  let  a  sheet  of  cardboard,  on  which  arcs  of  concentric 
circles  have  been  drawn,  be  fastened  to  the  projecting  board  or 

2 


INSTRUMENTAL  APPLIANCES 

platform,  where  the  meridian  line  is  desired.  The  center  of 
these  arcs  is  to  be  taken  as  one  point  in  the  meridian,  and  to 
find  a  second,  proceed  somewhat  as  follows : 

Suspend  a  plumb  line,  so  that  when  the  point  of  the  bob  comes 
to  rest  over  this  center,  the  line  itself  passes  centrally  across  the 
aperture  used.  Then,  rather  more  than  an  hour  before  apparent 
noon,  begin  to  watch  the  solar  image,  and  as  it  moves  to  the 
south,  mark  its  center  at  the  instants  when  it  coincides  succes- 
sively with  three  or  four  of  the  concentric  arcs.  In  like  manner, 
after  noon,  fix  points  on  the  same  arcs,  as  the  image  moves 
northward.  In  making  all  marks,  the  image  itself  should  be  the 
only  guide,  that  is,  no  time-piece  should  be  consulted. 

Now,  theoretically  considered,  if  the  sun's  declination  were 
constant  during  observation,  the  two  points  thus  marked  on 
any  one  arc  ought  to  be  equally  distant  from  the  meridian;  and, 
BO  if  the  chord  connecting  them  is  bisected,  a  second  point  in  the 
meridian  is  obtained.  (See  Dialling,  Encyclopaedia  Britannica.) 
Notwithstanding  the  sun's  motion,  however,  and  the  unavoidable 
errors  in  locating  the  center  of  the  image,  the  mean  position,  de- 
rived from  the  bisection  of  several  arcs  should  give  quite  accurate 
results.  As  a  further  precaution,  it  is  well  to  repeat  the  operation 
on  another  date,  and  finally  after  the  line  has  been  drawn,  it 
should  be  tested  by  actual  observations. 

7.  Meridian. stand. — If  two  posts,  about  five  feet  high,  are 
set  firmly  in  the  ground  on  either  side  of  the  meridian,  they  pro- 
vide a  stable  support  for  a  shelf,  making  altogether  a  high  stand 
for  the  use  of  jointed-rods  (§  11).     The  shelf  should  be  removed 
easily,  in  order  to  leave  an  open  space  to  the  north  and  south 
whenever  desired,  and  care  must  be  taken  to  have  it  level  and 
the  direction  of  its  sides  true  to  the  points  of  compass. 

8.  Plumb  lines. — Two  plumb  lines  may  be  employed  in  observ- 
ing transits,  by  sighting  so  that  they  appear  as  one.     Such  lines 
are  used  mainly  in  finding  time  from  the  sun,  and  a  few  bright 
stars,  and  it  is,  therefore,  essential  that  they  should  be  placed 

3 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

Accurately  in  the  plane  of  the  meridian,  and  remain  perfectly 
steady  during  observation.  The  problem  of  light  also  requires 
special  consideration.  The  sun  is  so  bright  that  when  it  is  ob- 
served, a  large  part  of  its  light  must  be  cut  off;  and  at  night  the 
lines  must  be  illuminated,  but  without  much  diminishing  the 
star's  brightness.  Electric  lights,  on  account  of  the  ease  with 
which  they  are  adjusted  and  controlled,  are  preferable,  but  small 
kerosene  lanterns  will  do  very  well  (§  62,  Obs.  2). 

Fish  tackle  is  good  material  for  plumb  lines,  whether  they  are 
«oarse  or  fine;  and  the  thickness  desired,  as  it  depends  largely 
upon  the  distance  between  the  lines,  the  objects  to  be  observed, 
and  the  method  of  lighting,  is  best  found  by  experiment. 

9.  Plumb-line  booth. — The  three  requisites  for  serviceable 
plumb  lines,  steadiness,  proper  lighting,  and  position  in  the 
meridian  are  most  readily  attained  by  placing  the  lines  under 
shelter.  A  plumb-line  booth,  in  order  to  accommodate  two  ob- 
servers at  the  same  time,  and  a  larger  number  at  different  times, 
should  have  a  floor  space,  at  least  eight  by  ten  feet,  and  a  height 
not  less  than  six  feet.  The  floor  must  be  firm  and  level,  and  if 
it  is  painted  white,  the  meridian  line  is  more  easily  established 
and  plainly  marked. 

Convenience  and  independence  in  observing  are  facilitated  if 
the  booth  is  divided  into  two  compartments  by  a  partition  passed 
north  and  south  through  the  center.  Each  part  is  then  entered 
Iby  a  door  on  the  north,  and  opposite,  in  the  south  wall  are  narrow 
•openings,  which  are  protected,  when  the  booth  is  not  in  use,  by 
wooden  shutters.  These  can  be  made  in  two  or  three  sections, 
.and  at  night,  if  the  upper  one  is  left  open,  there  is  an  unimpeded 
passageway  for  the  star's  light.  On  the  other  hand,  for  day  work, 
ithis  aperture  may  be  covered  with  colored  glass,  dark  enough 
for  looking  directly  at  the  sun. 

Plumb  lines  are  conveniently  hung  from  screw  hooks  in  the 
ceiling.  Locate  first  the  two  in  the  meridian,  one  near  the  middle 
of  the  south  opening,  and  the  other,  two  or  three  feet  farther 
north.  On  either  side  of  the  latter,  a  little  distance  from  it,  east 

4 


INSTRUMENTAL  APPLIANCES 

and  west,  i.  e.,  in  the  prime  vertical  (§  15,  9),  suspend  two  other 
lines.  Thus,  three  sets  of  reference  lines  are  obtained;  for  by 
sighting,  each  north  line  is  made  to  coincide  with  the  one  at  the 
south.  If  there  has  been  good  success  in  placing  these  line» 
accurately,  they  constitute  no  mean  form  of  transit  instrument;, 
for  the  final  determination  of  time  is  made  to  depend  upon  several 
transits,  independently  noted  (§  62,  Obs.  1,2). 

To  provide  for  off-meridian  transits  by  different  observers,, 
several  additional  lines  may  be  placed  in  the  prime  vertical  just 
mentioned,  each  pair  being  distinguished  by  some  such  designa- 
tion as,  "south  line  and  that  from  screw  hook  No.  5."  Equipped 
in  this  manner,  the  two  compartments  give  opportunity  for 
noting  ten  or  more  transits  of  the  same  star  in  the  same  evening, 
facilities  that  are  especially  convenient  for  a  large  number  in. 
finding  the  length  of  the  sidereal  day  (§  63). 

10.  Home-made  transit  instruments. — A  home-made  telescope 
(Byrd,  Appendix),  or  any  small  telescope,  mounted  in  the  merid- 
ian, is  serviceable  as  a  transit  instrument.  It  should  be  given 
a  heavy  wooden  support  consisting  of  a  base  and  two  uprights 
(Fig.  1) .  The  telescope  tube  ought  to  be  fitted  permanently  inta 
the  horizontal  axis,  and  the  ends  of  the  latter,  which  rest  in  the 
wyes  of  the  uprights,  should  be  as  nearly  as  possible  circular  in 
form  and  equal  in  diameter.  The  whole  frame  can  be  fixed  in 
position  on  a  meridian  platform  by  stationary  blocks,  placed  one 
at  each  corner,  and  if  they  are  pierced  by  coarse  screws,  they 
give  means  for  adjusting  in  azimuth  (§  85). 

One  way  to  light  the  field  of  view  is  to  hang  a  small  lantern  on 
a  movable  upright,  placed  to  one  side,  a  little  distance  from  the 
object-glass.  This  upright  may  be  passed  through  a  block  on  a 
stand,  and  provided  with  a  set  screw,  so  as  to  be  clamped  at 
different  altitudes  as  the  telescope  is  moved  up  and  down.  The 
lantern,  so  nearly  in  the  line  of  sight,  must  be  carefully  adjusted 
and  hooded  that  it  may  not  inconvenience  the  observer. 

The  striding  level  employed  with  the  instrument  is  shown  in 
position  in  Fig.  1.  It  is  made  by  mounting  a  level  tube,  like 

5 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

that  of  a  carpenter's  level,  in  the  middle  of  a  "turned"  axis, 
having  about  the  same  diameter  as  that  of  the  horizontal  axis 
on  which  the  wyes  of  its  legs  rest. 


FIG.  1. — Home-Made  Transit  Instrument. 

When  not  in  use,  the  level  and  the  telescope  with  its  axis  must 
be  kept  where  they  are  fully  protected  from  the  weather,  and  it 
is  desirable  to  cover  the  frame  at  least  with  enamel  cloth  (§1). 

ii.  Jointed-rods  and  protractor. — A  simple  device  for  measur- 
ing altitude  and  azimuth  is  obtained  by  riveting  together  two 

6 


INSTRUMENTAL  APPLIANCES 

wooden  rods,  like  rulers.  For  the  width  of  ^  inch,  18  inches  is  a 
convenient  length.  One  free  end  should  be  pointed,  and  each 
rod  move  easily  on  the  other,  though  not  too  easily;  for,  after 
they  have  been  opened  to  measure  the  sun's  altitude,  for  instance, 
they  must  be  kept  unchanged  in  direction  till  the  angle  between 
them  is  read  off  from  a  protractor  (§  19). 

The  foundation  for  the  protractor  may  be  a  wooden  disk  about 
15  inches  in  diameter,  with  one  side  curved  to  prevent  warping. 
On  the  other  side,  which  should  be  as  nearly  plane  as  possible, 
mount  a  paper  protractor,  divided  into  quadrants  and  graduated 
at  least  to  degrees.*  The  whole  should  then  be  finished  with 
several  coats  of  shellac  and  varnish. 

12.  The  Circles. — An  altazimuth  instrument  is  the  most  ser- 
viceable for  measuring  angles  in  reference  to  the  horizon,  as  one 
pointing  at  a  body  gives  both  altitude  and  azimuth.  An  instru- 
ment of  this  kind,  called  the  Circles,  is  sufficiently  accurate  for 
naked-eye  observers.  As  illustrated  in  Fig.  2  on  the  following 
page,  it  consists  of  an  upiight  shaft,  about  five  feet  high,  and  two 
circles,  one  vertical,  for  measuring  altitude,  the  other  horizontal  for 
measuring  azimuth.  The  former,  made  like  the  protractor  de- 
scribed in  the  preceding  section,  is  attached  to  the  upper  part  of  the 
shaft,  and  when  adjustments  are  properly  made,  the  line  connect- 
ing the  zero  marks,  from  which  altitudes  are  reckoned,  should  be 
truly  horizontal.  The  other  circle,  which  forms  the  base  of  the  in- 
strument, is  made  somewhat  larger  and  braced  on  the  under  side 
with  heavy  cleats.  Its  graduations  are  clock- wise  and  continu- 
ous, but  those  of  the  vertical  circle  are  divided  into  quadrants. 

The  upright,  which  turns  in  the  lower  circle,  is  shod  with  iron 
and  fits  into  an  iron  socket  so  as  practically  to  plumb  itself,  and 
an  offset  near  the  top  brings  both  pointers  into  the  same  vertical 
plane. 

This  instrument  is  commonly  used  on  a  meridian  line  already 
established,  and  in  or  near  a  building  containing  a  large  amount 

*  Accurate  protractors  of  good  size  may  be  obtained  from  Keuffel  and 
Esser,  New  York. 

7 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

of  iron,  otherwise  it  might  be  well  to  have  all  metal  parts  made 
of  zinc,  as  the  pocket  compass  could  then  be  used  in  adjusting. 


Fia.  2.— The  Circles. 

13.  Horizontal  sun-dial. — The  sun-dial,  illustrated  in  Fig.  3, 
has  one  marked  peculiarity;  the  style  is  in  reality  a  shaft  of  sun- 
light. To  economize  space,  as  well  as  to  aid  in  adjustment,  the 
base  is  half,  instead  of  a  whole  circle.  It  has  a  radius  of  about 
15  inches,  and  is  constructed  like  the  base  of  the  Circles  (§  12), 
with  a  block  placed,  however,  at  the  middle  of  the  diameter  for 
supporting  the  style,  or  what  should  perhaps  be  called  the  frame 
of  the  style.  This,  in  the  instrument  described,  is  simply  part 

8 


INSTRUMENTAL  APPLIANCES 

of  a  wooden  ruler,  22  inches  long,  with  an  aperture  rather  more 
than  an  eighth  of  an  inch  wide,  extending  nearly  its  whole  length. 
By  means  of  an  accurate  triangular  pattern,  the  ruler  is  placed 
so  that  its  angular  elevation  above  the  dial  face  is  just  equal  to 
the  latitude  of  the  place.  It  should  be  attached  to  the  block  by 


FIG.  3.— Open-Style  Sun-Dial. 

screws,  so  that  slight  adjustments  are  possible,  and  a  plumb  line 
is  serviceable  in  testing  whether  the  central  line  of  the  aperture 
lies  in  the  same  vertical  plane  as  the  noon  line. 

In  adjusting  the  horizontal  sun-dial,  it  is  customary  to  place 
the  completed  instrument  upon  a  meridian  line  already  deter~ 
mined.  The  opposite  method  may,  however,  be  employed. 
Thus,  after  the  style  is  in  place,  but  before  any  graduations  are 

9 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

made,  the  base  may  be  fixed  securely  just  where  the  dial  is  to  be 
used,  and  the  meridian  line  drawn  directly  upon  it,  somewhat  as 
described  in  §  6.  Then  the  sheet  of  paper  with  the  required 
graduations  is  simply  fastened  to  the  base,  with  the  noon  line 
passing  through  the  center  of  the  style  and  coinciding  with  the 
meridian  line. 

The  main  graduations  are  in  hours,  and  these  are  subdivided 
into  five-minute  spaces.  Morning  hours  are  marked  to  the  right, 
as  one  faces  south,  and  afternoon  hours  to  the  left,  extending 
from  6h  A.M.  to  6h  P.M.;  but  the  extreme  divisions  in  either 
direction  are  rarely  used,  for  sun-dial  readings  should,  as  a  rule, 
be  taken  during  the  three  hours  before  noon  and  the  three  after, 
so  as  to  obtain  a  strong,  sharp  shadow,  or  a  bright  beam  of 
light.  The  moving  shadow  or  beam  of  light  takes  the  place  of 
hands  on  a  clock,  and  to  tell  time  by  the  dial  is  to  note  their 
position  in  reference  to  the  graduations.  To  read  the  sun-dial 
commonly  means  to  record  the  time  from  a  watch  when  they  lie 
centrally  over  one  of  the  graduations,  or  symmetrically  between 
two  of  them. 

Since  the  graduations  vary  with  the  latitude,  the  angular 
deviation  of  each  line  from  the  noon  line  must  be  calculated  for 
the  place  where  the  dial  is  to  be  used.  The  common  formula  is 
that  given  under  "Dialling"  in  the  "Encyclopaedia  Britannica," 

i.e.,  tan  a  =  tan  t  sin  <£, 

where  0  is  the   latitude  of  the  place,  t  the  time,  and  a  the 
corresponding  arc  on  the  dial. 

14.  Miscellaneous  appliances. — In  addition  to  the  home- 
made instruments  already  described,  the  following  appliances 
are  important:  straight  edge,  pocket  compass,  steel  scale,  trans- 
parent protractor,  carpenter's  level,  orrery,  celestial  globe,  opera- 
glasses,  and  small  telescope.  The  level  is  required  in  adjusting 
the  common  gnomon  and  sometimes  with  other  instruments. 
An  orrery  is  needed  to  illustrate  the  real  movement  of  the  planets 
in  reference  to  the  sun,  and  their  different  aspects,  conjunction, 

10 


WORKS  OF  REFERENCE 

opposition,  and  quadrature.  The  celestial  globe  is  serviceable 
in  many  ways,  especially  in  checking  the  observed  positions  of 
heavenly  bodies  and  finding  their  rates  of  motion.  It  aids  also 
in  supplementing  the  phenomena  seen  at  one  place  by  those 
visible  at  the  equator,  poles,  and  other  distant  points.  In  a 
word,  the  celestial  globe  checks,  connects,  extends,  and  gener- 
alizes the  beginner's  observations. 

Magnifying  power  for  studying  the  heavens  is  perhaps  best 
given  at  first  by  opera-glasses.  Those  having  a  power  of  two 
or  three  diameters  show  detail  on  the  moon,  and  resolve  some 
double  stars  and  star  clusters.  A  telescope  is  the  last,  rather 
than  the  first  instrument  to  be  obtained.  The  danger  is  that  it 
will  be  only  a  pretty  toy,  but  even  as  a  plaything  it  has  its  uses, 
and  one  can  be  put  together  with  little  expense.  For  a  full 
description  of  a  method  that  may  be  employed,  see  Appendix  A 
of  the  writer's  "  Laboratory  Manual  in  Astronomy."  Instead, 
however,  of  making  the  tubes,  much  labor  is  saved  by  using 
mailing  tubes,  or  tin  tubes,  of  suitable  size.  In  the  second  chap- 
ter of  this  manual  are  to  be  found  also  additional  details  about 
the  simple  kinds  of  apparatus  considered  in  the  foregoing  pages. 

Works  of  reference  should  include  a  large  star  atlas,  large  map 
of  the  moon,  the  "American  Ephemeris  and  Nautical  Almanac" 
(§  34),  and  some  elementary  work  on  practical  astronomy  like, 
"Comstock's  Field  Astronomy  for  Engineers,"  or  "Campbell's 
Elements  of  Practical  Astronomy."  Each  student  should  have 
small  star-maps  with  reference  circles,  and  a  common  almanac. 
For  the  eastern  section  of  the  country,  the  Old  Farmer's  Almanac 
is  serviceable  and  Dr.  Jayne's  for  the  south  and  west.  The 
former  has  the  advantage  of  being  free  from  medical  advertise- 
ments, and  that  is  also  a  characteristic  of  the  Atlantic  Monthly 
Almanac. 

15.  Preliminary  definitions — The  following  definitions  contain 
nothing  original,  but  so  many  of  them  are  needed  immediately 
in  observing  that  they  are  entered  here  in  concise  form  for  the 
convenience  of  teachers  and  students. 

11 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

1.  The^celestial^sphere  of  astronomers  is    one  with  infinite 
radius,  and  finite  space  as  center.     Its  inner  concave   surface 
forms  our  heavens  where  sun,  moon,  stars,  and  other  heavenly 
bodies  appear. 

2.  The  zenith  is  the  point  in  which  an  imaginary  plumb  line, 
passed  through  the  observer's  position  and  prolonged  upward, 
cuts  the  celestial  sphere. 

3.  The  nadir  is  the  point  exactly  opposite  the  zenith  in  the 
celestial  sphere  underneath. 

4.  The  visible  horizon  is  the  line  where  the  earth  and  sky  seem 
to  meet. 

5.  The  sensible  or  true  horizon  is  the  great  circle  in  which  the 
plane,  passing  through  the  observer's  eye  and  perpendicular  to 
the  plumb  line,  cuts  the  celestial  sphere  (Young,  Art.  15). 

6.  Vertical  circles  are  great  circles  of  the  celestial  sphere,  which 
pass  through  the  zenith,  and  are  perpendicular  to  the  horizon. 

7.  The  foot  of  a  vertical  circle  is  the  point  where  it  intersects 
the  horizon. 

8.  The  vertical  circle  passing  through  the  pole  is  the  celestial 
meridian  (19,  20). 

9.  The  prime  vertical  is  that  vertical  circle  which  is  at  right 
angles  to  the  meridian. 

10.  The  altitude  of  a  heavenly  body  is  its  angular  distance 
above  the  horizon,  measured  on  a  vertical  circle  passing  through 
the  body. 

11.  The  zenith  distance  of  a  heavenly  body  is  the  complement 
of  its  altitude. 

12.  The  azimuth  of  a  heavenly  body  is  the  arc  on  the  horizon, 
measured  from  the  south  point  (22)  westward  to  the  foot  of  the 
vertical  circle,  passing  through  the  body. 

13.  When  the  altitude  is  zero,  the  other  coordinate  (33)   is 
often  called  amplitude  and  reckoned  from  the  east  or  west  point. 

14.  The  north  and  south  poles  of  the  celestial  sphere  are  the 
points  where  the  earth's  axis  prolonged  pierce  the  sphere. 

15.  The  celestial  equator  is  the  great  circle  of  the   sphere, 
passing  midway  between  the  poles. 

12 


PRELIMINARY  DEFINITIONS 

16.  Parallels  of  declination  are  small  circles  of  the   sphere 
which  are  parallel  to  the  celestial  equator. 

17.  Hour-circles,  called  also  circles  of  declination,  are   great 
circles  of  the  sphere  passing  through  its  poles,  and  perpendicular 
to  the  celestial  equator. 

18.  The  foot  of  an  hour-circle  is  the  point  where  it  intersects 
the  celestial  equator. 

19.  The  hour-circle  which  passes  through  the  zenith   is  the 
celestial  meridian  (8). 

20.  In  general,  the  celestial  meridian  is  defined  as  the  great 
circle  of  the  sphere  which  passes  both  through   the  pole  and 
through  the  zenith. 

21.  The  southing  of  a  heavenly  body  is  the  instant  when  it 
crosses  the  meridian,  and  it  signifies  also  the  crossing  itself. 

22.  The   four    cardinal    points    are,    the    north    and    south 
points,   where   the   meridian   intersects   the   horizon,    and   the 
east  and  west  points,  where  the  prime  vertical  intersects   the 
horizon. 

23.  The  declination  of  a  heavenly  body  is  its  angular  distance 
north  or  soiSh  of  thlTcelestial  equator,  measured  on  the  hour- 
circle  passing  through  the  body.     It  is  called  positive  and  marked 
with  the  plus  sign  when  north,  negative  and  marked  with  the 
minus  sign  when  south. 

24.  The  hour-angle  of  a  heavenly  body  is  measured  westward 
on  the  celestial  equator,  from  the  foot  of  the  meridian  to  the  foot 
of  the  hour-circle  passing  through  the  body. 

25.  The  ecliptic  is  the  great  circle  of  the  celestial  sphere  in 
which  the  sun  appears  to  make  its  annual  circuit  of  the  heavens, 
or  it  is  the  circle  marked  out  on  the  sphere  by  a  plane  passing 
through  the  earth's  orbit! 

26.  The  equinoxes   are   the   points   where   the   ecliptic    arid 
equator  intersect,  and  they  are  also  the  instants  of  time  when 
the  sun  reaches  these  intersections.     That  is,  when  it   crosses 
the   equator   going   north,   that   instant   is   called    the   vernal 
equinox,  and  when  it  crosses  going  south,  that  instant  is  called 
the  autumnal  equinox. 

13 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

27^  The  solstices  are  the  points  in  the  ecliptic  farthest  north 
and  south,  and  they  are  also  the  instants  of  time  when  the  sun 
reaches  these  points. 

28.  The  angle  at  which  the  ecliptic  is  inclined  to  the  celestial 
equator  is  called  the  obliquity  of  the  ecliptic. 

29.  The  right  ascension  of  a  heavenly  body  is  the  arc  on  the 
celestial  equator,  measured  eastward  from  the  vernal  equinox 
to  the  foot  of  the  hour-circle  passing  through  the  body. 

30.  Circles  of  latitude  are  great  circles  of  the  celestial  sphere 
passing  through  the  pole  of  the  ecliptic,  and  perpendicular  to 
that  circle. 

31.  The  celestial  latitude  of  a  heavenly  body  is  its  angular 
distance  north  or  south  of  the  ecliptic,  measured  on  the  circle  of 
latitude  passing  through  the  body. 

32.  The  celestial  longitude  of  a  heavenly  body  is  the  arc  on 
the  ecliptic,  measured  eastward  from  the  vernal  equinox  to  the 
foot  of  the  latitude-circle  passing  through  the  body. 

33.  The  coordinates  of  a  heavenly  body  are  the  two  angular 
measures  which  fix  its  position  on  the  sphere.     Thus,  altitude 
and  azimuth  are  a  pair  of  coordinates,  so  also  are  right  ascension 
and  declination. 

16.  Independence  in  observing. — To  see  with  one's  own  eyes, 
and  to  make  one's  own  record  of  what  is  seen  are  essentials 
in  astronomical  observing.     Consultat'on  about  estimates  and 
measures  is  not  admissible,  nor  comparison  of  results  as  they  are 
entered  in  the  notes.     In  so  far  as  any  observation  is  biased  by 
what  others  see  and  do,  in  so  far  it  is  worthless  (Byrd,  §  2). 
Independence  is  the  corner  stone  of  good  observing. 

17.  Rules  for  recording. — The  note-book  record  constitutes 
an  integral  part  of  every  observation,  and  should  be  made  accord- 
ing to  the  following  rules. 

1.  Begin  the  record  for  each  evening  on  a  new  page. 

2.  At  the  head  of  every  page,  name  the  place  of  observing, 
day  of  week,  day  of  month,  and  the  year. 

14 


RULES  FOR  RECORDING 

3.  Name  in  connection  with  each  observation  any  instrument 
employed,  describing  it  if  possible  when  first  used. 

4.  Write  out  notes  in  detail,  so  that  others  following  them 
could  take  the  same  observation  in  the  same  way. 

5.  Keep  all  records  of  direct  observation  in  pencil,  and  make 
in  ink  any  corrections  necessary.     This  is  the  fundamental  record 
which  no  copy  can  supersede. 

6.  Make  no  use  of  an  eraser  in  recording  essentials,   but  if 
something  has  been  set  down  inadvertently,  cross  it  out,   and 
interline  above. 

7.  In  general,  do  not  reject  an  observation  once  taken.     The 
fact  that  it  is  discordant  when  compared  with  others  of  the  same 
series  is  never  a  reason  for  rejection. 

8.  Decide  on  the  last  figure  to  be  retained  in  making  any  kind 
of  record,  and  then  abide  by  that  limit.     Thus,  if  right  ascension 
on  the  globe  is  to  be  read  to  minutes,  do  not  at  times  write  halves 
or  thirds  of  a  minute.     Bear  in  mind  also  that  zero  is  really  a 
figure,  and  should  be  entered  just  as  3  or  8  would  be. 

9.  The  fraction  beyond  the  last  figure  retained  should   be 
counted  as  a  whole  unit,  if  it  is  over  a  half,  if  less,  it  should  be 
rejected.      When  it  is  exactly  half,  follow  some  definite  rule  so 
that  it  will  be  retained  about  as  often  as  discarded.     Thus,  for 
example,  count  a  half  a  whole,  if  it  "evens  up"  the  last  figure, 
otherwise  reject  it. 

The  precepts  of  this  rule  apply  also  in  making  numerical  re- 
ductions of  observations. 


15 


CHAPTER   II. 

POINTS  IN  SUN'S  DIURNAL  PATH;  CONSTELLATIONS  IDENTIFIED;  STAR-MAPS; 
DIFFERENT  KINDS  OF  TIME;  STANDARD  MERIDIANS  AND  TIME  SECTIONS; 
ALMANACS;  CELESTIAL  GLOBE;  LATITUDE;  CHECKS  FOR  ALTITUDE  AND 
AZIMUTH. 

1 8.  Sun's    diurnal    path    without    instruments. — The    daily 
oourse  of  the  sun  in  the  heavens  is  so  closely  connected  with 
length  of  day  and  change  of  seasons  that  it  is  of  first  importance 
in  naked-eye  observing.    An  ideal  determination  would  require 
several  positions  to  be  fixed  between  rising  and  southing  (§  15, 
&1),  and  southing  and  setting;    but  the  two  latter  bring  out 
clearly  the  shift  in  the  path  of  the  sun  from  month  to  month, 
nor  are  instruments  absolutely  essential.     A  rough  value  for 
noon  altitude  (§  15,  8,  10}  may  be  obtained  by  using  a  porch 
pillar  or  the  trunk  of  a  tree  as   a  gnomon,   and   a  series  of 
rising  or  setting  points  can  be  traced  along  the  horizon  by 
eye  estimates  only  (Byrd,  §  106). 

19.  Sun's  noon  altitude  and  azimuth  at  setting  with  jointed- 
rods  and  protractor. — Having  chosen  dark  glasses  suited  to  the 
eyes,  place  the  blunt  arm  of  the  jointed-rods  (§  11)  on  the  me- 
ridian stand  (§7),  and  holding  it  firmly  in  the  horizontal  plane, 
move  the  other  one  up  and  down  till  its  whole  line  of  direction 
points  to  the  sun.    Note  for  each  rod  whether  its  inner  or  outer 
edge  was  used  in  sighting,  and  place  the  intersection  of  the  two 
actually  employed  at  the  center  of  the  cross  on  the  protractor 
which  fixes  the  center  of  the  graduations.    Let  the  edge  of  one 
rod  coincide  with  the  line  of  zero  degrees,  and  at  the  edge  of 
the  other  read  the  required  angle.     Whole  degrees  are  given 
directly  by  the  graduations,  but  tenths  must  usually  be  esti- 
mated.   If  the  habit  has  been  formed  of  estimating  in  quarters 

16 


POINTS  IN  SUN'S  DIURNAL  PATH 

and  thirds,  call  a  quarter  two-tenths,  a  third  three-tenths  but 
two-thirds  seven-tenths.  (See  also  §  17,  9). 

In  making  the  evening  observation,  keep  both  rods  in  the 
plane  of  the  stand  with  the  blunt  arm  directed  due  north  (§  15, 
##),  when  the  sun  sets  south  of  west,  but  when  it  sets  north  of 
west,  turn  the  blunt  arm  to  the  latter  point  so  as  to  avoid  meas- 
uring an  angle  greater  than  90°. 

OBSERVATION — Smith  College  Observatory,  Northampton, 
Mass.,  Friday,  Oct.  5,  1906.  I  measured  the  sun's  noon  altitude 
today  and  its  azimuth  at  setting,  using  jointed-rods  and  pro- 
tractor as  described  above.  The  results  obtained  and  the 
checks  from  almanac  (§  28)  and  globe  (§  29)  are  as  follows: 


TABLE  I. — SUN'S  NOON  ALTITUDE  AND  AZIMUTH  AT  SETTING. 


TIME. 

ALTITUDE 
AT  NOON. 

CHECK 

FROM 

ALMANAC. 

TIME. 

AZIMUTH 
AT  SUNSET. 

CHECK 

FROM 

GLOBE. 

Ilh45m 

43°.5 

5h   9m 

S39.  2 

52 

44  .0 

10 

83  .0 

55 

43  .8 

11 

83  .5 

Means  11   51 

43  .8 

43°.l 

5   10 

83.2 

82°.3 

(B.  G.  F.) 

Dark  glasses,  rods,  and  protractors  need  be  provided  for  only 
about  half  the  number  that  are  to  observe  on  the  same  day,  as 
some  will  be  recording  their  notes  while  others  are  sighting  and 
measuring.  One  meridian  stand  meets  the  needs  of  four  or  five 
students,  but  there  should  be  ample  space  on  a  firm  level  surface 
for  resting  protractors. 

Not  only  is  sun  noon  the  time  for  locating  the  most  critical 
point  in  the  sun's  diurnal  path;  but  it  is  also  favorable  for 
determining  latitude  (§§43,  44),  drawing  a  north  and  south  line 
(§§  6,  61),  and  finding  the  error  of  a  watch  (§  61,  Obs.,  §  62,  Obs. 
1),  so  it  is  desirable  to  make  careful  provision  for  observing  at 
this  time. 

17 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

20.  Constellations  identified. — Star-maps  with  fundamental 
reference  lines  (§21)  should  be  used  in  beginning  the  study  of 
the  constellations.  Having  a  list  of  those  that  are  to  be  identified 
first,  fix  in  mind  their  names,  note  the  maps  where  they  are  to 
be  found,  and  the  groups  of  stars  that  characterize  them,  as  the 
"dippers"  in  Ursa  Major,  and  Ursa  Minor,  and  the  row  of  three 
bright  stars  in  Aquila. 

In  the  evening,  let  the  place  for  observing  be  as  free  as  pos- 
sible from  artificial  lights.  Begin  with  some  conspicuous  con- 
stellation near  the  horizon.  Identify  its  prominent  stars  and 
when  these  are  recognized  with  certainty,  make  use  of  them  in 
picking  out  another  constellation,  and  so  pass  to  a  number,  along 
the  horizon  and  higher  up  in  the  heavens. 

After  ten  or  fifteen  have  been  found  thus,  there  should  be  a 
short  exercise  in  a  lighted  room,  so  that  the  configurations  seen 
in  the  sky  can  be  compared  with  those  on  the  maps. 

OBSERVATION. — S.  C.  O.,  Northampton,  Mass.,  Monday, 
Sept.  30,  1907.  Notes  were  not  required  on  the  first  evening 
when  constellations  were  found  in  the  sky,  and  so  the  list  given 
below  includes  all  that  have  been  identified  on  both  the  first  and 
second  night  of  observing. 

TABLE  II. — CONSTELLATIONS  IDENTIFIED. 

About  the  Pole.     Near  East  Horizon.        In  the  South.      Near  West  Horizon. 

1.  Ursa  Major.         1.  *Andromeda.  1.  Sagittarius.  1.  Bootis. 

2.  Ursa  Minor.        2.  Triangulum.  2.  fAquila.  2.  Corona. 

3.  Cassiopeia.  3.  fPegasus.  3.  *Capricornus.  3.  Scorpio. 

4.  Perseus.                4.  *Pisces.  4.  Delphinus.  4.  "Ophiuchus. 
Near  the  zenith,  *Cygnus,  Lyra.  5.  *Serpens.  5.  Hercules. 

Constellations  were  not  considered  identified  till  I  had  found 
them  independently  both  in  the  sky  and  on  the  map.  Those 
marked  with  a  star,  I  found  in  the  first  place  by  myself;  and  for 
those  marked  with  a  dagger,  I  found  more  stars  than  were 
pointed  out  to  me.  (A.  E.  S.) 

18 


STAR-MAPS 

21.  Star-maps. — Maps  of  the  heavens,  though  in  some  re- 
spects like  those  of  a  common  geography,  require  careful  exami- 
nation before  observations  begin  (§  20).  Most  of  the  important 
points  are  illustrated  by  Map  IV  of  Young's  Uranography,  where 
the  heavy  line  through  the  middle  of  the  page  represents  the 
celestial  equator  (§  15,  15).  From  it,  heavenly  bodies  are  located 
by  measuring  eastward  along  the  line,  and  to  the  north  or  south 
of  it,  as  in  referring  towns  to  the  terrestrial  equator.  To  aid  in 
making  measures,  two  sets  of  auxiliary  lines  are  drawn,  one 
parallel,  the  other  at  right  angles  to  the  celestial  equator.  Those 
parallel  are  called  parallels  of  declination  (§  15,  16),  and  those 
perpendicular,  hour-circles  (§  15,  17).  There  may  be  an  in- 
definite number  in  either  set.  On  the  map  named,  parallels  of 
declination  are  separated  by  10  degrees,  and  the  number  of 
degrees  that  each  line  lies  north  or  south  of  the  equator  is 
marked  on  either  side  of  the  page.  The  hour-circles, 
separated  by  15  degrees  of  arc  measure  or  one  hour  of  time, 
are  numbered  with  Roman  figures,  from  I  to  XXIV  or  0, 
beginning  at  the  vernal  equinox  (§  15,  26). 

The  eastward  measurement,  corresponding  to  longitude  on 
the  earth,  is  called  right  ascension  (§  15,  29),  and  all  celestial 
objects  on  the  hour-circle  II  or  XX,  for  instance,  have  a  right 
ascension  of  two  or  twenty  hours  respectively.  The  measure- 
ment north  or  south,  corresponding  to  latitude,  is  called  decli- 
nation (§15,  23),  and  objects  on  the  10  or  20  degree-line  above 
the  equator  have  north  declination  of  10  or  20  degrees.  The 
right  ascension  and  declination  of  objects  between  the  lines  may 
be  estimated  by  the  eye,  or  measured  by  strips  of  rectangular 
paper  (§39). 

The  constellations  in  which  the  stars  have  been  grouped  from 
time  immemorial  are  outlined  on  most  star-maps  by  irregular 
boundary  lines,  much  as  the  confines  of  states  are  indicated  on 
terrestrial  maps.  Other  lines  are  often  used  to  mark  put  striking 
configurations  of  stars  as,  "the  cross  of  Cygnus"  and  "the  great 
square  of  Pegasus."  Some  of  the  bright  stars  have  individual 
names,  as  Vega  in  Lyra,  and  Altair  in  Aquila;  others  are  desig- 

19 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

nated  by  numbers  or  English  letters,  but  for  most  stars  given  on 
small  maps,  Greek  letters  alone  are  used,  a  being  usually  as- 
signed to  the  brightest  star  in  a  constellation.  Thus,  Vega  is 
also  a  Lyra  (Young,  Art.  422). 

22.  Apparent,  mean,  and  standard  time. — The  sun  in  the  sky 
controls  apparent  or  sun  time.  The  instant  when  it  crosses  the 
meridian  marks  apparent  noon,  and  at  any  moment  its  hour- 
angle  (§  15,  24)  is  apparent  time.  Since,  however,  the  real  sun 
does  not  mark  off  days  and  hours  of  exactly  the  same  length,  it 
is  necessary,  in  regulating  clocks  and  watches,  to  make  use  of  a 
fictitious  or  mean  sun,  which  moves  at  a  perfectly  uniform  rate 
(Young,  Art.  55). 

This  mean  sun  controls  mean  time  which  never  differs  largely 
from  sun  time  (§  36).  The  instant  when  it  crosses  the  meridian 
of  a  place  marks  local  mean  noon,  and  at  any  moment  its  hour- 
angle,  reckoned  from  the  local  meridian,  is  local  mean  time. 
This  kind  of  time  was  long  used  in  the  practical  affairs  of  life; 
but  some  years  before  the  close  of  the  last  century,  railway 
travel  gave  rise  to  the  troublesome  question,  "How  far  on  either 
side  does  the  time  of  one  meridian  extend?"  This  difficulty  was 
finally  settled  by  establishing  standard  meridians  exactly  one 
hour  apart,  and  standard  time  now  in  general  use  is  thus  de- 
fined. The  mean  sun  controls  standard  as  well  as  local  mean 
time.  The  instant  when  it  crosses  the  standard  meridian  of  a 
given  time  section  marks  standard  noon,  and  at  any  moment  its 
hour-angle,  reckoned  from  the  standard  meridian,  is  the  standard 
time  of  that  section. 

From  the  definition  of  local  time,  it  follows  that  exactly  at  the 
standard  meridian,  standard  time  is  local  time,  so  standard  time 
may  also  be  defined  as  the  local  time  at  the  standard  meridian. 

.23.  Standard  meridians  and  time  sections. — Standard  me- 
ridians for  reckoning  time  are  in  use  in  all  parts  of  the  world, 
being  uniformly  named  by  the  number  of  degrees  they  are  east 
or  west  of  the  Greenwich  meridian.  The  four  in  our  country  are 

20 


TIME  SECTIONS 

75,  90,  105,  and  120  degrees  west  of  Greenwich,  each  giving  its 
time  to  the  territory  lying  within  about  1\  degrees  of  longitude 
on  either  side  of  it.  There  are  then  four  standard  times,  desig- 
nated as  follows : 

Eastern  time,  with  Stand.  Merid.     75°  or  5h  west  of  Greenwich 

Central       "         "       "  "  90     "  6      "      " 

Mountain  "         "       "  "  105     "  7      "      " 

Pacific        "         "       "  "  120     "  8      "      "          " 

Hereafter  in  observations  and  exercises,  reference  is  usually 
made  to  these  times  by  their  initial  letters,  as  E.  s.  T.  for  the 
first  and  c.  s.  T.  for  the  second. 

A  fifth  division  of  standard  time,  that  of  the  60th  meridian  is 
employed  in  eastern  Maine  for  points  situated  east  of  Vance- 
boro.  As  here  indicated,  the  change  from  the  time  of  one  me- 
ridian to  that  of  another  is  not  usually  made  at  the  meridian 
precisely  midway  between  two  standard  meridians,  but  along 
an  irregular  line  depending  upon  the  exigencies  of  railway  systems 
and  connections.  There  are  also  places  in  our  country  which 
retain  local  time,  using  standard  as  railway  time.  This  is  likely 
to  occur  where  the  difference  between  the  two  times  is  large,  that 
is,  where  a  town  or  city  is  about  equally  distant  from  two  stand- 
ard meridians.  Detroit,  Mich.,  in  longitude  5h  32m  W.  (Ap- 
pendix) for  a  long  period  made  use  of  both  kinds  of  time. 

In  spite,  however,  of  some  deviations  from  the  theoretical 
scheme,  the  rule  commonly  holds  that  the  time  kept  at  any 
place  is  that  of  the  standard  meridian  which  is  nearest  in  longi- 
tude. Thus,  Omaha,  Neb.,  in  longitude,  6h  24m  W.  keeps  the 
time  of  the  6h  meridian,  being  a  little  nearer  that  standard 
meridian  than  the  one  farther  west. 

24.  Jayne's  Almanac. — Jayne's  Almanac  is  one  of  the  best  of 
the  small  almanacs  for  reference  in  elementary  astronomy. 
(Byrd,  Chap.  III.)  On  the  first  page  are  the  technical  symbols 
and  abbreviations  used  in  the  calendar,  with  the  necessary  ex- 
planations. The  current  page  for  the  month,  as  is  seen  by  re- 

21 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

ferring,  for  instance,  to  September,  contains  a  number  of  facts 
about  different  heavenly  bodies.  There  is  a  column  given  to 
aspects  of  planets  and  southing  (§  15,  21)  of  bright  stars;  for 
the  sun,  there  are  times  of  rising  and  setting,  "sun  fast"  (§  36) 
and  length  of  day;  for  the  moon,  times  of  rising,  setting,  and 
southing,  place  on  the  sphere,  and  diagram  of  moonlight  hours. 
The  latter  is  helpful  in  preparing  for  observations.  Thus,  it 
shows  at  a  glance  that  Sept.  29,  1911,  was  favorable  for  lunar 
study,  as  the  crescent  moon  was  visible  between  6  and  10  P.  M. 
On  the  other  hand,  any  evening  of  the  preceding  week  was  suited 
for  observing  planets,  stars,  and  Milky  Way,  for  there  was  then 
no  moonlight  to  interfere. 

Jayne's  Almanac  is  calculated  for  different  latitudes,  and  so 
is  adapted  to  different  sections  of  the  country.  For  example, 
that  for  latitude  40°  is  the  one  to  employ  in  Illinois,  Kansas, 
Colorado  and  other  states  named  on  the  calendar  page.  The 
times  given  are  the  local  times  of  the  meridian  5  hours  west  of 
Greenwich;  but  several  hours  of  longitude  have  little  effect  on 
the  local  time  of  astronomical  phenomena  (Byrd,  §  42).  So  it 
follows  that  this  almanac,  rightly  selected  for  latitude,  would 
be  directly  applicable  in  many  states  if  local  time  were  employed. 
For  standard  time,  corrections  are  required  (§  38). 

25.  The  Old  Farmer's  Almanac. — This  almanac  is  designed  for 
New  England  and  can  be  closely  adapted  to  all  sections  by  a 
table  of  differences  in  longitude,  given  in  the  introduction.  In 
any  locality,  however,  it  will  be  found  convenient  for  reference, 
as  it  contains  rather  more  than  the  average  amount  of  astro- 
nomical data,  carefully  arranged.  For  each  month,  there  are 
two  calendar  pages  which,  in  addition  to  the  usual  phenomena 
of  sun,  moon,  and  planets,  include  the  sun's  declination  from 
day  to  day. 

Note  that  "sun  fast"  here  is  not  the  equation  of  time  (§  36), 
but  the  difference  between  apparent  and  standard  time  (§  22), 
so  that  the  change  from  one  to  the  other  is  made  directly  without 
passing  through  mean  time  (Byrd,  §  37,  Ex.). 

22 


CELESTIAL  GLOBE 

Whatever  almanac  is  employed,  a  copy  should  be  placed  on 
file  each  year,  as  there  is  often  occasion  to  refer  to  back  numbers. 

26.  Celestial  globe. — The  celestial  globe  gives  in  miniature  a 
representation  of  the  celestial  sphere  (§  15,  1),  but  as  it  is  the 
outer  surface  which  is  shown,  what  is  to  the  left,  i.  e.,  east  on  a 
star-map,  is  to  the  right  on  the  globe,  though  for  both,  east  is 
always  toward  increasing  right  ascensions.     Except  for  change 
in  direction,  the  constellations  appear  much  as  on   star-maps, 
and  there  are  the  usual  reference  circles.    The  celestial  equator 
is  commonly  divided  into  15-degree  or  hour-spaces  by  24  hour- 
circles    which    are    numbered    consecutively   from    the    vernal 
equinox,  parallels  of  declination  are  separated  from  the  equator 
and  from  each  other  by  10-degree  spaces  (§  21);   and  on  some 
globes,  degrees  on  the  ecliptic  (§  15,  25)  are  numbered  on  the 
upper  side  in  thirties  to  facilitate  the  reading  of  celestial  longi- 
tude (§  15,  82),  and  dots  below  mark  the  approximate  position 
of  the  sun  for  each  day  of  the  month. 

The  graduated  ring  which  holds  the  globe  in  its  supporting 
frame  serves  as  the  celestial  meridian  (§  15,  20),  and  the  wide 
plate  of  the  frame,  for  the  horizon  (Young,  Arts.  524-526). 

27.  Declination  of  zenith  equal  latitude. — According  to  one  of 
the  common  definitions,  latitude  equals  the  altitude  of  the  pole 
at  the  given  place.     It  follows,  therefore,  that  latitude   equals 
the  declination  of  the  zenith.     This  is  shown  by  Fig.  4  where, 

1.  N  Z  S  is  the  upper  half  of  the  meridian. 

2.  N  and  S  north  and  south  points. 

3.  P  the  pole  and  Z  the  zenith. 

4.  Q  the  point  where  the  equator  intersects  the  meridian. 

Now,  NZ  or  NP+ PZ  =  90°,  as  it  is  the  distance  from  zenith 
to  horizon,  and  PQ  or  PZ-fQZ  =  90°,  as  it  is  the  distance  from 
the  pole  to  the  equator.  Therefore  NP+PZ  =  PZ+QZ,  or  NP 
=  QZ.  But  NP  is  the  altitude  of  the  pole,  and  QZ  is  the  decli- 
nation of  the  zenith,  for  it  is  the  angular  distance  of  the  zenith 

23 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

from  the  celestial  equator  measured  on  the  hour-circle  (§  15,  19) 
passing  through  the  zenith  (§  15,  23).  The  declination  of  the 
zenith,  therefore,  equals  the  latitude. 


Q 


Two  minor  inferences  follow,  first,  for  any  position  of  the  globe, 
the  zenith  (§  15,  2)  is  just  opposite  that  point  on  the  meridian 
ring  where  the  reading  for  declination  equals  the  latitude  of 
the  place.  Second,  the  altitude  of  the  equator  at  the  point 
where  it  intersects  the  meridian,  QS,  Fig.  4,  is  equal  to  the  co- 
latitude,  for  it  is  the  complement  of  QZ,  the  equal  of  the  latitude. 

28.  Sun's  noon  altitude  checked  from  decimation. — Since  the 
noon  altitude  of  the  sun  is  measured  on  the  meridian,  if  it  is 
above  the  equator,  its  altitude  may  be  represented  by  SS',  if 


FIG.  5. 

below  by  SS",  Fig.  5,  and  the  corresponding  declinations,  by 
QS'  and  QS".  The  latter  quantities,  as  they  can  be  taken  from 
an  almanac,  may  be  considered  known  quantities.  Moreover, 
QS  is  known  whenever  the  latitude  is  known,  as  it  is  its  comple- 

24 


CHECKS  FOR  ALTITUDE  AND  AZIMUTH 

ment  (§  27),  so  the  altitude  SSf  is  obtained  by  adding  Q/S'Jto 
QS,  and  the  altitude  SS",  by  subtracting  QS"  from  QS.  Since, 
however,  south  declinations  are  negative,  the  general  rule  for 
finding  altitude  is,  add  algebraically  the  sun's  declination  for 
the  date  to  the  meridian  altitude  of  the  celestial  equator  at  the 
given  place. 

EXERCISE. — Given  the  sun's  noon  altitude  43°. 8  as  observed, 
Oct.  5,  1906,  Northampton,  Mass.  (§  19);  required  the  check 
from  the  sun's  declination. 

The  different  steps  may  be  arranged  as  follows: 

Latitude  of  place,  or  declination  of  zenith,  42°. 3 


Meridian  altitude  of  celestial  equator,  47  .7 

Sun's  declination  fr.  p.  24,  0.  F.  Almanac,  —4  .6 


Sun's  altitude  f  r.  declination,  43  . 1 

Sun's  altitude  fr.  observation,  43  .8 


Error  of  observation,  0  .7 

In  like  manner,  a  check  is  obtained  for  the  meridian  altitude 
of  the  moon  (Byrd,  §  32,  Ex.  2),  or  for  any  body  with  known 
declination. 

29.  Altitude  and  azimuth  checked  on  globe. — Since  the  most 
important  altitude,  that  on  the  meridian,  can  be  checked  arith- 
metically from  declination  (§  28),  the  globe  is  not  often  required 
for  this  coordinate  (§  15,  88),  but  it  is  in  constant  requisition  in 
checking  azimuth  (§  15,  12},  especially  the  sun's  azimuth  at 
setting.  One  method  consists  simply  in  bringing  to  the  horizon 
plate  the  dot  which  marks  approximately  the  sun's  position  for 
the  day  (§  26),  and  reading  the  degrees  for  azimuth  found  just 
opposite.  It  is  better,  however,  to  take  account  of  the  altitude 
of  the  sun  when  the  observation  was  made;  for  while  at  sunset, 
that  is  theoretical  zero,  practically  it  is  a  degree  or  more,  owing 
partly  to  the  fact  that  the  visible  horizon  (§  15,  4)  is  seldom  in 

25 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

the  plane,  determined  by  the  level,  from  which  observations  are 
made  (§  15,  5),  and  partly  to  the  necessity  of  beginning  the 
record,  when  the  sun  is  a  little  above  the  horizon,  in  order  to 
obtain  several  readings  (§  30,  Obs.).  A  check  that  is  usually 
satisfactory  is,  therefore,  obtained  as  follows : 

Orient  the  globe  for  latitude  (§  40),  mark  off  the  observed 
altitude  near  one  end  of  a  narrow  strip  of  paper  which  serves  as 
a  vertical  circle  (§  15,  6),  pass  the  other  end  through  the  zenith 
point  (§  27),  and  turn  the  globe  till  the  upper  mark  for  altitude 
coincides  with  the  dot  for  the  sun,  and  the  lower,  with  the  horizon 
plate.  The  azimuth  read  opposite  the  latter  mark  gives  the 
required  check. 

If  very  precise  results  are  desired,  orient  the  globe  for  the 
time  and  place  of  observation  (§  40),  and  see  that  it  is  held  in 
position,  i.  e.,  "clamped,"  by  crowding  something  soft  between 
the  ball  and  horizon  plate.  Take  from  the  Ephemeris,  for  the 
given  date,  the  coordinates  of  the  sun,  locate  it  on  the  globe 
(§51,  Ex.  3),  and  through  the  point  thus  fixed,  and  that  for  the 
zenith,  pass  a  strip  of  paper  as  above.  The  intercept  between 
the  plate  and  the  sun's  place  gives  its  altitude,  which  may  be 
evaluated  in  degrees  by  laying  the  paper  on  one  of  the  graduated 
circles  of  the  globe.  The  corresponding  azimuth  is  read,  of 
course,  where  the  paper  strip  meets  the  horizon  plate. 

This  is  a  method  that  serves  in  checking  any  altitude  and 
azimuth  of  any  body,  though  for  values  between  the  meridian 
and  horizon,  no  further  test  is  usually  required  than  that  given 
by  plotting  on  rectangular  paper  (§  80). 


26 


CHAPTER  III. 

SUN'S  DIURNAL  PATH;  PLANETS  IDENTIFIED;  CONSTELLATIONS  MAPPED; 
AMERICAN  EPHEMERIS;  CHANGING  FROM  ONE  KIND  OF  TIME  TO  AN- 
OTHER; PLOTTING  ON  STAR-MAPS;  ORIENTING  CELESTIAL  GLOBE. 

30.  Sun's  diurnal  path  with  Circles. — In  setting  up  the  instru- 
ment (§  12)  on  the  meridian  stone,  it  is  well  to  handle  the  base 
and  upright  separately  to  prevent  jars.  Adjust  so  that  the 
graduations  for  0°  and  180°  come  exactly  over  the  meridian 
line,  and  level  the  base  as  accurately  as  possible,  using  a  car- 
penter's level  for  testing,  if  there  are  no  level  vials  in  the  base 
itself. 

To  "set"  on  the  sun,  turn  the  upright  shaft,  and,  with  a  hand 
on  the  clamp  at  the  back,  move  the  pointer  of  the  vertical  circle 
till  it  seems  to  pierce  the  sun,  being  careful  meanwhile  not  to 
use  the  upright  in  any  way  as  a  support.  It  should  be  left  free 
to  plumb  itself.  After  the  final  clamping  has  been  made  and 
both  hands  removed,  see  that  the  direction  of  the  upper  pointer 
is  unchanged;  and  then  be  on  guard  against  disturbing  either 
pointer  in  the  few  moments  between  calling  "time"  to  the  re- 
corder, and  making  readings  for  altitude  and  azimuth.  These 
should  be  taken  opposite  the  center  of  each  pointer,  but  if  it 
is  more  convenient  to  employ  the  edge,  add  or  subtract  half 
the  pointer's  diameter. 

Two  observations,  one  with  the  vertical  circle  in  a  given 
position,  the  other  after  it  has  been  turned  180°  in  azimuth, 
are  required  to  fix  a  single  point  (Byrd,  §  3);  and  two  points, 
either  rising  and  southing  or  southing  and  setting,  are  desirable 
in  tracing  any  diurnal  path  of  the  sun  (§  18).  Either  pair  of 
these  critical  points  may  be  allowed  to  suffice  in  fixing  four  of 
the  six  paths  that  should  be  located  during  the  year;  but  the 
other  two  ought  to  have  three  or  more  intermediate  positions, 

27 


FIRST  OBSERVATIONS  IN  ASTRONOMY 


at  hourly  intervals,  so  as  to  bring  out  clearly  the  form  of  the 
solar  path  between  the  meridian,  and  the  horizon  on  one  side. 

OBSERVATION. — S.  C.  O.,  Northampton,  Mass.,  Tuesday,  May 
21,  1907.  I  take  today  a  seven-point  path  of  the  sun,  with  the 
Circles  adjusted  on  the  second,  south  meridian  stone.  A  strong 
wind  interferes  with  accurate  settings. 

The  data  in  full,  obtained  at  noon  and  sunset,  with  the  usual 
checks  (§§  28,  29),  are  as  follows: 

TABLE  III. — DATA  FOR  SUN'S  DIURNAL  PATH,  NORTHAMPTON,  MASS. 


DATE, 
May  21,  1907. 

ALTITUDE 
AT  NOON. 

AZI- 
MUTH. 

CIRCLE. 

TIME. 

ALTI- 
TUDE. 

AZIMUTH 

AT  SETTING. 

ClBCLB. 

Ilh49n> 
50 
52 
53 

68°.  8 
67  .8 
67  .4 
68  .6 

2°.0 
2  .3 
4  .0 
3  .0 

West 
East 
East 
West 

6h46m 
47 
49 
50 

3°.l 
2  .1 
2  .0 
2  .3 

115°.  2 
115  .0 
115  .0 
116  .0 

North 
South 
South 
North 

Means  11    51 

68  .2 

2.  8 

6   48 

2  .4 

115  .3 

Ck.  fr.  Decl. 

67  .7 

Ck.  fr.  Globe 

114  .6 

Error 

0  .5 

Error 

0  .7 

The  mean  results  of  the  five  intermediate  positions  are: 


Time  

12h  56m 

2h  4m 

3hcm 

4h32m 

5h34m 

Altitude  

64°.0 

53°.7 

42°.6 

26°.8 

15°.2 

Azimuth  

39  .1 

63  .4 

78  .4 

93  .7 

103  .5 

(E.  W.  J.) 


In  taking  a  series  of  observations  like  that  above,  the  instru- 
ment used,  after  being  carefully  adjusted,  should,  if  possible, 
remain  undisturbed  throughout  the  whole  operation.  Points 
between  the  meridian  and  the  horizon  are  satisfactorily  fixed 
by  two  readings,  with  opposite  positions  of  the  vertical  circle. 

28 


SUN'S  DIURNAL  PATH 

31.  Sun's  diurnal  path  with  solar-image  gnomon. — The  re* 
quired  observations,  with  this  gnomon,  consist  merely  in  placing 
a  dot,  a  number  of  times,  at  the  center  of  the  sun's  image. 


Fw.  6. 


The  method  of  deriving,  from  these  dots,  the  sun's   coordi- 
nates, is  illustrated  by  Fig.  6,  where, 

1.  0  is  the  center  of  aperture  used. 

2.  SM,  the  meridian  line  in  O's  vertical  plane. 

3.  S,  south  point  of  meridian  line. 

4.  B,  C,  M,  D,  F,  G,  H,  points  marked  in  observing. 

5.  SB,  SC,  etc.,  bases  of  triangles,  right-angled  at  S. 

6.  BO,  CO,  etc.,  lines  showing  the  direction  of  the  sun. 

7.  P  III  N,  semicircular  protractor. 

29 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

When  the  protractor  has  been  properly  adjusted,  with  the 
center  of  graduations  at  S,  and  the  radius  of  zero  degrees  coin- 
ciding with  meridian,  No.  Ill,  azimuths  are  read  directly  at 
the  points  where  the  base  lines,  as  SB  and  SC,  intersect  the 
graduated  arc.  In  making  these  readings,  one  point  requires 
attention.  Since  the  sun  is,  of  course,  on  the  opposite  side  of  the 
meridian  from  its  image,  when  that  is  found  a  little  west  of  the 
meridian  line,  as  at  C,  the  sun's  azimuth  is  nearly  360°,  or  it 
may  be  expressed  as  a  small  negative  angle. 

To  obtain  altitudes,  note,  for  example,  that  in  the  right- 
angled  triangle,  OSB,  BO  is  the  line  of  direction  toward  the 
sun,  and  BS  is  in  the  plane  of  the  horizon,  therefore  the  angle 
OBS  is  the  sun's  angular  elevation  above  the  horizon,  that  is, 
its  altitude,  when  the  center  of  the  image  is  at  B.  If  desired, 
this  angle  may  be  obtained  without  calculation.  Thus,  lay  off 
SO  and  SB  on  plotting  paper  at  right  angles  to  each  other  and 
in  correct  proportion,  mark  the  line  BO,  and  then  place  a  trans- 
parent protractor  on  the  paper,  so  as  to  read  the  angle  at  B, 
or  cut  out  the  paper  form  OBS  and  measure  the  angle  from  the 
mounted  protractor,  described  in  §  11. 

The  solution  by  trigonometry  is  really  shorter,  for,  as  OSB 
is  a  right  angle, 


and  if  the  numerical  values  of  the  following  observations  are 
substituted,  the  computation  is  as  follows  : 

log  20.  00,  1.3010 

log   7.56,  0.8785 

log  tan  69°  18,     0.4225 

OBSERVATION.  —  Normal  College,  New  York,  N.  Y.,  Thursday, 
May  29,  1913.  The  gnomon  that  I  employ  to  find  the  sun's 
path  is,  in  general,  like  that  described  in  §  5.  The  "plate 
glass"  is  about  4  ft.  wide,  but  its  height  is  only  25  in.,  and 
the  upper  part  is  not  available  on  account  of  the  shadow  of  the 

30 


SUN'S  DIURNAL  PATH 

frame.  The  projecting  board  is  6.5  ft.  long,  2.5  ft.  wide,  and 
has  three  meridian  lines  marked  on  it.  I  make  use  of  the  one 
numbered  III,  reckoning  from  the  east,  and  at  six  different 
times,  fix  by  dots  the  center  of  the  sun's  image. 

To  find  the  corresponding  coordinates  of  the  sun,  azimuths 
are  read  from  a  protractor  and  altitudes  calculated  as  described 
above.  The  mean  of  three  measures  of  the  common  side  OS  is 
20.00  in.,  and  the  other  data  obtained  are  as  follows: 

TIMES.  BASES.  AZIMUTHS.  ALTITUDES. 

nh2im  7in.  56  -23°. 2                 69.3 

51  6    .94  -  3  .5                  70.9 
12    21  7    .28  +17  .2                  70.0 

52  8    .36  +36  .2                  67.3 

1  24  10    .17  +51  .0  63.0 

2  15  14    .08  +67  .8  54.8 

From  the  azimuths  and  altitudes  in  the  last  two  columns,  I 
plot  the  sun's  path  for  today  on  rectangular  paper,  and  find  that 
a  smooth  curve  passes  almost  exactly  through  all  of  the  six 
points  (§  80).  (J.  C.  D.) 

The  second  observation  is  so  near  noon  that  the  angle  [for 
altitude,  70°.9,  may  be  checked  from  the  Ephemeris.  There, 
the  sun's  declination  for  the  given  date  is  found  to  be  21°.6, 
making  the  theoretically  correct  altitude  70°.8  (§  28).  While 
no  observations  were  taken  late  in  the  afternoon,  and  there  is 
thus  uncertainty  in  the  prolonged  curve,  it  indicates  that  the 
sun  set  between  30°  and  35°  north  of  the  west  point.  The  globe 
check  gives  30°. 

With  regard  to  dates  for  observing  the  diurnal  path  of  the 
sun,  it  is  a  good  arrangement  to  locate  three  in  the  fall,  the  last 
near  the  winter  solstice  (§  15,  27) ;  and  three  in  the  spring,  one 
near  the  equinox  (§15,  26)  and  the  third  not  far  from  the  summer 
solstice  (§  80).  As  a  rule,  three  weeks  or  more  should  intervene 
between  different  observations,  though  an  extra  path  may  well 
be  inserted  at  equinoxes  or  solstices. 

All  instruments  are  used  to  better  advantage  if  they  are 
examined  before  observations  are  taken.  Thus,  with  the  Cir- 

31 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

cles,  it  is  well,  in  some  day  laboratory  period,  to  note  how  the 
graduations  are  made  and  numbered,  to  practice  taking  read- 
ings; and  if  possible,  measure  the  altitude  and  azimuth  of  some 
terrestrial  object  where  there  is  no  need  of  dark  glasses  or 
illumination. 

32.  Bright  planets  identified. — The  five  planets  known  to  the 
ancients,  Mercury,  Venus,  Mars,  Jupiter,  and  Saturn  are  bright 
bodies,  readily  seen  by  the  unaided  eye.  There  are  various  ways 
of  identifying  them.  If  Sirius  and  a  few  other  conspicuous  stars 
are  known,  it  is  often  possible  to  pick  out  Venus  and  Jupiter  by 
their  brightness  alone;  and  in  general,  when  any  bright  star-like 
body  is  seen  in  the  heavens,  where  no  corresponding  object  is 
found  on  the  map,  it  is  probably  a  planet,  and  any  doubt  can 
be  removed  by  looking  a  few  nights  later  to  see  whether  it  has 
changed  its  position  in  reference  to  neighboring  stars. 

The  small  almanacs  (§§  24,  25)  give  data  that  are  helpful  in 
finding  a  single  planet,  or  in  locating  all,  and  distinguishing  one 
from  another.  It  is  well  to  know  beforehand  about  each  one, 
whether  it  is  a  "morning"  or  an  "evening"  star  (Byrd,  §  31), 
whether  it  is  near  conjunction,  opposition,  quadrature,  or 
greatest  elongation  (Young,  Arts.  289  and  290);  and  how  it  is 
placed  with  regard  to  the  horizon,  that  is,  when  it  rises,  souths 
or  sets. 

One  of  the  quickest  and  surest  methods  of  identifying  is  to 
take  from  the  Ephemeris  (§  34)  the  coordinates  of  the  body  re- 
quired, plot  them  approximately  on  a  star-map  (§  39),  and 
then  look  in  the  sky,  near  the  reference  stars.  If  a  bright  object 
is  found  close  to  the  map  place,  and  its  coordinates,  estimated 
directly,  agree  with  those  given  in  the  Ephemeris,  it  is  in  all 
probability  the  planet  sought.  Still,  it  is  not  amiss  to  look 
again  on  another  night  and  see  if  it  has  moved.  For  those  who 
are  not  very  familiar  with  the  heavens,  it  is  often  puzzling  to 
know  when  and  where  to  look,  even  after  the  planet's  place  has 
been  found  as  above  on  a  map.  The  simplest  way,  perhaps,  is 
to  refer  to  a  planisphere  or  to  an  atlas,  like  "Proctor's  Half- 

32 


BRIGHT  PLANETS  IDENTIFIED 

Hours  with  the  Stars,"  which  depicts  the  principal  constellations 
in  reference  to  horizon  and  zenith  at  different  hours,  on  a  number 
of  dates  throughout  the  year. 

Instead  of  maps,  the  celestial  globe  may  be  employed  for 
locating  the  body  (§  51),  and  if  it  is  oriented  for  the  time  and 
place  of  observation  (§  40),  it  shows  the  position  of  a  planet  with 
regard  to  the  horizon,  as  well  as  among  the  stars.  The  globe 
gives  also  another  means  of  identifying;  for,  when  the  altitude 
and  azimuth  of  a  body  have  been  observed,  it  is  only  necessary 
to  plot  these  coordinates  on  the  oriented  globe,  and  compare 
the  place  thus  fixed  with  that  obtained  from  the  Ephemeris. 
This  is  a  satisfactory  way  to  identify  Mercury  and  fix  its  place 
among  the  stars  (§51,  Ex.  l). 

The  common  dictum,  that  planets  do  not  twinkle,  gives  little 
if  any  help  to  beginners,  in  making  identifications. 

OBSERVATION. — Denver,  Colo.,  Friday,  Feb.  25, 1910.  To  aid 
in  finding  Saturn  tonight,  reference  is  made  to  Jayne's  Almanac. 
There  it  is  seen  (p.  9)  that  the  planet  comes  into  conjunction 
with  the  sun  April  16;  and  interpolation  between  the  times  of 
setting  given  for  February  and  March  makes  the  time  for  Feb. 
25,  9h  20m  P.  M.  (§  50,  Ex.  l),  standard  as  well  as  local  (§  38, 
Ex.  4).  Saturn  should,  therefore,  be  visible  in  the  west  in  the 
early  evening. 

I  look  in  that  quarter  of  the  sky  at  7h  P.  M.,  and  find  an 
object  brighter  than  others  in  the  vicinity,  which  I  think  is  the 
planet.  Its  place  is  carefully  fixed  by  a  sketch,  including  several 
of  the  bright  stars  in  Pisces.  About  a  week  later,  I  find  the 
same  object  again,  near  the  same  stars,  but  as  its  angular  direc- 
tion from  the  reference  line  has  very  perceptibly  changed  I  con- 
clude it  is  a  planet.  It  cannot  be  Mercury  or  Venus,  for  at  this 
time  they  are  morning  stars  (Old  Farmer's  Almanac,)  nor  can 
it  be  Jupiter,  for  that  planet  does  not  rise  till  after  8  o'clock 
(Jayne's  Almanac).  It  must  then  be  either  Mars  or  Saturn, 
but  the  former  does  not  set  till  nearly  midnight,  and  this  object 
will  reach  the  horizon  long  before  then,  so  it  is  without  doubt 
the  planet  Saturn.  (M.  S.  S.) 

33 

3 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

33.  Constellations  mapped. — Before  sketches  are  made  of  in- 
dividual constellations,  as  many  as  fifteen  should  be  easily  recog- 
nized in  the  sky  (§20).  Those  that  are  to  be  drawn  first  should 
be  studied  beforehand  from  star-maps,  in  the  daytime,  and  the 
Greek  alphabet  must  be  thoroughly  mastered  (p.  6,  "Young's 
Uranography"). 

To  avoid  delay  and  perplexity  in  beginning  a  map,  and  to 
insure  its  proper  location  on  the  page,  a  reference  line  may  be 
fixed  by  a  card  pattern.  This  is  simply  a  piece  of  stiff  card- 
board that  fits  exactly  two  sides  of  the  record  page,  the  other 
part  being  cut  in  such  shape  that  dots  marked  on  its  edge  fix 
the  places  of  two  prominent  stars  of  the  constellation.  Working 
from  these,  either  directly  or  indirectly,  the  other  stars  of  the 
map  are  located  by  estimates  of  distance  and  angle,  more  de- 
pendence being  placed  upon  the  former.  As  a  unit  of  distance, 
take  a  star-line,  that  is  the  line  joining  two  stars,  and,  if  possible, 
let  it  be  near  the  distance  to  be  measured,  and  approximately 
in  the  same  direction  with  regard  to  the  horizon  (Byrd,  §  6). 
Estimates  are  also  facilitated  by  taking  pains  in  choosing  refer- 
ence stars.  Thus,  the  eye  judges  more  accurately  as  to  whether 
objects  are  in  line  than  of  any  other  configuration  (§  46,  Obs.), 
and  angles  of  90°  or  J  90°  are  more  easily  estimated  than  others. 

For  the  note-book  record,  it  is  a  good  arrangement  to  enter 
fundamental  data  and  explanations  on  one  page,  and  the  map 
itself  on  that  opposite.  As  many  as  seven  stars  should  be  in- 
cluded, and,  since  accuracy  in  their  relative  positions  is  the 
prime  requisite,  attention  during  observation  should  center  on 
locating  dots  for  them  as  carefully  as  possible.  Later,  in  some 
day-laboratory  period,  the  proper  symbols  for  magnitude  may 
be  inserted. 

In  the  evening,  the  first  exercise  is  to  identify  with  certainty 
the  stars  to  be  included.  If  the  constellation  to  be  mapped  is 
Aquila,  known  already  by  its  rows  of  three  bright  stars,  others 
will  be  found  somewhat  as  follows : 

The  star-line  7/3  prolonged  beyond  /3,  rather  more  than  its 
own  length,  meets  the  fairly  bright  star  0,  and  a  line  from  that 

34 


CONSTELLATIONS  MAPPED 

passing  toward  the  Milky  Way,  and  making  an  acute  angle 
with  yd,  goes  nearly  through  17  and  5.  To  find  f,  pass  a  line 
through  5,  nearly  parallel  to  #7  and  extending  about  as  far  in 
the  same  direction.  An  eighth  star,  X,  is  fixed  by  prolonging  76 
its  own  length  beyond  6.  As  a  check,  note  that  yB5£  mark  out 
approximately  an  oblique  parallelogram. 

OBSERVATION. — 519  Oakland  Avenue,  Pasadena,  Calif.,  Tues- 
day, Oct.  27, 1908.  Taking  aTras  the  reference  line,  I  have  mapped 
Puppis  in  Argo-Navis,  as  shown  in  Fig.  7,  on  the  following  page. 
In  all,  17  eye-estimates  of  distance  and  angle  have  been  made, 
but  the  following  are  the  most  fundamental : 

1.  Za7TK  =  180°,  St.  Line    5.      Zf<r7r  =  90° 

2.  7TK  =  iair  6.  {<r  =  (nr 

3.  Za7rf  =  90°  7.      Zarf  =  180° 

4.  7r£  =  fa7T  8.  aT  =  %av 

Several  double  stars  in  Puppis  and  the  cluster  about  a  deserve 
notice.  For  these  objects,  as  well  as  for  two  or  three  faint  stars, 
opera-glasses  were  used.  (L.  B.) 

The  first  maps  demand  much  patient  effort.  It  requires  prac- 
tice to  carry  in  mind  a  number  of  specifications  traced  on  the 
map,  and  bring  back  from  the  sky  the  required  estimates.  It 
also  demands  self-control  to  work  independently,, to  make  esti- 
mates of  distance  and  angle  without  any  inquiry  as  to  what 
values  others  are  obtaining  and  recording,  but  independence  is 
of  vital  importance  in  astronomical  observing  (§  16). 

Since  all  naked-eye  study  of  the  heavens  is  founded  on  a 
knowledge  of  the  constellations,  they  must  receive  careful  and 
repeated  attention.  About  35  ought  to  be  mastered  so  that 
they  are  easily  recognized  at  all  times  and  seasons,  no  matter 
how  they  are  placed  with  regard  to  the  horizon.  Maps  should 
be  made  of  rather  more  than  half  this  number,  and  the  others, 
identified  by  seven  or  more  stars. 

34.  American  Ephemeris. — The  almanac  used  by  surveyors, 
navigators,  and  astronomers  is  a  large  volume  containing  hun- 
dreds of  pages.  That  published  at  Washington  for  our  country 

35 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

is  called  the  "American  Ephemeris  and  Nautical  Almanac,"  and 
even  in  an  elementary  course  is  indispensable  for  reference. 


*/> 


.  •'.  ei 
•A 


+P 

*r 


Fro.  7.     Puppis  in  Argo-Navis. 

36 


AMERICAN  EPHEMERIS 

The  first  part  of  the  book  is  devoted  to  phenomena  connected 
with  the  Greenwich  meridian,  and  the  sections  most  needed  for 
reference  are  those  giving  the  right  ascension  and  declination  of 
the  planets  throughout  the  year,  and  the  same  coordinates  for 
the  moon  at  every  hour  of  Greenwich  mean  time.  Immediately 
following  the  latter,  there  is  a  tabulation  of  the  times  of  lunar 
phases  for  each  month;  and  near  the  end  of  this  first  part  is  the 
mean  longitude  of  the  moon's  ascending  node,  which  is  of  use  in 
-showing  graphically  the  position  of  the  moon's  path  on  the 
celestial  sphere  (§  57,  final  Par.). 

Part  II,  which  is  based  on  the  Washington  meridian,  contains 
a  standard  star-catalogue,  including  both  mean  and  apparent 
places.  The  differences  between  the  two  are  inappreciable  on 
the  globe,  and  so  the  former  are  commonly  used  in  fixing  posi- 
tions connected  with  naked-eye  observing  (§  51,  Ex.  3),  but 
apparent  right  ascensions  should  be  employed  in  finding  time 
from  star  transits  (§  62,  Obs.  2). 

Under  the  sun,  much  of  the  data  given  is  more  directly  ap- 
plicable in  our  country  than  the  corresponding  values  for  Green- 
wich. This  is  especially  true  of  the  "Equation  of  Time,"  which 
is  essential  in  passing  from  apparent  to  mean  time,  and  the 
reverse  (§  36).  In  like  manner  the  coordinates  under  "Transit- 
Ephemerides  of  Planets"  are  to  be  preferred  for  all  dates  given; 
for  others,  recourse  must  be  had  to  Part  I.  The  section,  "Moon- 
Culminations"  is  often  convenient  for  reference,  as  it  shows  at 
a  glance  whether  the  moon  "runs  high"  or  "low." 

Part  III,  entitled  "Phenomena,"  is  that  from  which  the 
makers  of  small  almanacs  derive  much  of  their  material.  There 
are  here  very  full  details  about  solar  and  lunar  eclipses,  occulta- 
tions  of  stars  by  the  moon,  phases  and  librations  of  the  moon; 
and  conjunctions  and  other  aspects  of  planets.  The  diagrams 
for  satellites,  especially  for  Jupiter's  system,  are  helpful  in 
identifying  these  objects  in  a  telescope.  At  the  close  of  this 
part,  though  hardly  belonging  to  it,  is  an  alphabetical  list  of 
places,  with  latitudes  and  longitudes,  where  a  number  of 
observatories  are  located. 

37 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

Three  of  the  six  tables,  given  in  the  latter  part  of  the  Ephem- 
eris,  require  notice.  Table  I  is  used  in  finding  the  latitude  of  a 
place  from  off-meridian  altitudes  of  Polaris  (§78);  Table  II  con- 
tains the  corrections  for  reducing  the  hours,  minutes,  and  seconds 
of  sidereal  time  to  the  corresponding  mean  solar  interval;  and  from 
Table  III,  in  like  manner,  are  taken  the  corrections  required  in 
passing  from  a  mean  time,  to  the  equivalent  sidereal  interval. 

Except  for  problems  in  time  and  latitude,  data  from  the 
Ephemeris  should  usually  be  taken  only  to  the  nearest  minute 
of  time  and  tenth  of  a  degree  of  arc. 

35.  Civil  and  astronomical  days. — The  civil  day  is  the  one 
used  in  the  ordinary  affairs  of  life.     It  is  reckoned  from  mid- 
night to  midnight  in  periods  of  12  hours,  both  noon  and  mid- 
night being  called  twelve  o'clock.    The  astronomical  day  is  used 
in  the  Ephemeris  (§  34),  and  in  astronomical  records  and  calcu- 
lations (§  50,  Ex.  2,  §  60,  §  72,  Obs.  2).    It  begins  at  noon  when 
the  civil  day  of  the  same  date  is  12  hours  old,  and  is  reckoned 
continuously  through  24  hours.    The  day  of  the  month  is,  then, 
the  same  for  both  days  between  noon  and  midnight,  but  between 
midnight  and  noon,  the  astronomical  date  is  one  day  earlier. 
In  the  former  case  the  only  change  in  passing  from  one  date  to 
the  other  is  in  adding  or  dropping  the  p.  M.     To   illustrate   the 
latter,  let  it  be  required  to  find  what  civil  date  corresponds  to 
May  25,  19h  32m,  astronomical  time.    Since  at  12  o'clock,  mid- 
night on  the  25th,  the  civil  day,  May  26,  begins  with  zero  hours, 
12h  is  subtracted  from  19h,  and  one  added  to  the  date  number, 
making  the  civil  reckoning,  May  26,  7h  32m  A.  M. 

36.  Equation  of  time  and  "Sun  Fast." — The  differences  be- 
tween apparent  and  local  mean  time  (§  22)  is  known  as  the  equa- 
tion of  time.    It  is  constantly  changing,  but  so  slowly  that  for 
most,  if  not  all  naked-eye  exercises,  the  noon  value  for  Wash- 
ington may  be  used  through  the  day  and  throughout  the  country. 

"Sun  Fast"  or  "Sun  Slow"  given  in  the  small  almanacs  (§§  24, 
25)  is,  as  a  rule,  simply  the  equation  of  time  copied  from  the 

38 


ONE  TIME  CHANGED  TO  ANOTHER 

Ephemeris  (§  34),  to  the  nearest  minute,  the  signs  minus  and 
plus  being  replaced  by  fast  and  slow.  This  use  of  signs  in  the 
Ephemeris  is  like  that  made  by  astronomers  with  clock  and 
chronometer  errors.  Thus,  if  a  time-piece  is  fast,  its  error  is 
marked  minus,  if  slow,  plus. 

37.  Apparent  time  changed   to  local  mean  time  and  vice 
versa. — Apparent  time  is  changed  to  local  mean  time  by  adding 
or  subtracting  the  equation  of  time,  since  by  definition  that  is 
the  difference  between  them  (§  36).     In  applying  the  equation, 
the  signs  prefixed  are  to  be  taken  in  the  sense  that  apparent 
solar  time  is  fundamental,  and  mean  time  is  derived  from  it  by 
adding  the  equation  to  apparent  time  when  the  sign  is  plus,  and 
subtracting  it,  when  the  sign  is  minus  (Ephemeris  1914,  p.  713). 
For  example,  if  the  apparent    time   given  is  3h  llm  52s  p.  M., 
March  13,  1912,  the  equation  of  time  is,  +9m  37s  (Ephemeris, 
p.   519),   and   the   corresponding   mean   time   3h  21m  298    P.  M. 
Of  course,  if  the  latter  time  were  given  and  apparent  solar  time 
required,  the  9m  37s  would  be  subtracted.    So  it  must  be  fixed  in 
mind  that  the  signs  of  the  equation  do  not  necessarily  signify 
operations,  for  whether  a  plus  value  is  to  be  added  or  subtracted 
depends  upon  what  is  given  and  what  required. 

If  Jayne's  Almanac,  instead  of  the  Ephemeris  is  used,  the  re- 
duction can  be  carried  only  to  minutes,  for  sun  slow  is  given  as 
10m,  i.  e.,  only  to  the  nearest  minute  (§  36). 

38.  Local  mean   time  changed  to  standard  time  and    vice 
versa. — Standard  time  is  the  local  time  at  the  standard  meridian 
(§  22),  and  hence  all  questions  of   passing  from  one  standard 
time  to  another,  from  local  to  standard,  or  standard  to  local,  are 
reduced  to  the  simple  problem  of  changing  from  one  local  time  to 
another.    The  important  point  is,  then,  the  connection  between 
the  local  times  of  two  meridians.     In  general,  the  eastern  me- 
ridian has  the  faster  time;   for  the  sun,  moving  westward  in  its 
diurnal  course,  comes  there  first  and   marks  an  earlier  noon. 
To  find  definite  numerical  relations,  consider  two  stations,  A, 
on  the  eastern  meridian,  and  B  on  that  to  the  west.     It  is,  of 

39 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

course,  noon  at  A  when  the  sun  crosses  the  meridian  there,  but 
at  B,  noon  will  come  later  by  as  many  minutes  as  it  takes  the 
sun  to  pass  from  A  to  B.  This  interval  is  by  definition  the 
difference  in  longitude  between  the  two  meridians  (Young, 
Art.  61),  and  when  that  is  known,  either  local  time  is  readily 
obtained  from  the  other. 

In  the  two  examples  which  follow,  the  mean  sun  (§  22)  is  the 
one  to  think  of  as  controlling  the  different  times. 

EXAMPLE  1. — If  a  station,  A,  is  in  longitude  20m  east  of  5, 

(1)  When  it  is  noon  at  B,  what  is  the  time  at  A? 

(2)  In  general,  how  is  A' a  time  derived  from  5's? 

(3)  When  it  is  noon  at  A,  what  is  the  time  at  #? 

(4)  In  general  how  is  B's  time  derived  from  A's? 

After  the  sun  has  crossed  A' a  meridian,  marking  noon  there, 
it  takes  20m  to  pass  to  the  meridian  at  B,  and  meanwhile  the 
clock  at  A  has  gone  forward  20m,  so  when  it  is  noon  at  B,  A's 
time  is  20m  faster,  i.  e.,  12h  20m.  Since  the  relation  between 
the  times  of  the  two  stations  is  evidently  the  same  throughout 
the  day,  it  follows  that  for  any  instant  at  B,  the  corresponding 
time  at  A  is  20m  faster. 

On  the  other  hand,  when  it  is  noon  at  A,  it  still  lacks  20m  of 
noon  at  B,  so  B's  time  is  20m  slower  than  A's,  at  noon  and  at 
all  other  times  of  the  day. 

EXAMPLE  2. — If  the  meridian  passing  through  A,  20m  east  of 
B,  is  the  standard  meridian  for  B, 

1.  When  it   is  10h  A.  M.,  local  time  at  B}  what  is  the  corre- 
sponding standard  time  there? 

2.  When  it  is  5h  P.  M.,  standard  time  at  B,  what  is  the  cor- 
responding local  time? 

Since  standard  time  at  B  is  by  definition  the  local  time  at  its 
standard  meridian,  it  is  the  local  time  at  A,  but  that  is  20m 
faster  than  local  time  at  B  (Ex.  l),  so  when  it  is  10h  A.  M. 
local  time  at  B,  it  is  10h  20m  A.  M.  by  standard  time  there. 

Put  the  standard  time  at  B}  5h  P.  M.,  A's  local  time,  is  20m 
fast  for  B,  making  the  required  local  time  at  B,  4h  40m  P.  M. 

40 


ONE  TIME  CHANGED  TO  ANOTHER 

In  like  manner,  if  B's  meridian  is  taken  as  the  standard  for  At 
it  is  easy  to  follow  out  the  connection  between  local  and  standard 
times  for  places  having  their  standard  meridian  to  the  west. 
Therefore,  the  general  rules  for  passing  from  local  to  standard 
time  and  the  reverse  are  as  follows : 

If  local  mean  time  is  given  and  standard  time  required,  add  to 
the  local  mean  time  the  difference  in  longitude  between  the  two 
meridians,  when  the  standard  meridian  is  east  of  the  given  place, 
but  when  it  is  west,  subtract  this  difference. 

Conversely,  if  standard  time  is  given  and  local  mean  time  re- 
quired, subtract  from  standard  time  the  difference  in  longitude 
between  the  two  meridians,  when  the  standard  meridian  is  east 
of  the  given  place,  but  when  it  is  west,  add  this  difference. 

EXAMPLE  3. — Given  the  standard  time,  llh  4m  A.  M.,  at 
Raleigh,  N.  C.,  in  longitude  5h  15m  W.  (Appendix);  required  the 
corresponding  local  mean  time. 

From  the  longitude  given,  it  is  seen  at  once  that  Raleigh's 
standard  meridian  is  15m  east  of  the  place.  So  15m  is  subtracted 
from  the  standard  time,  giving  as  the  required  local  time  10h 
49m  A.  M. 

EXAMPLE  4. — According  to  Jayne's  Almanac,  the  southing 
of  Polaris,  i.  e.,  the  North  Star,  (§  15,  21)  came  at  10h  Om  P.  M. 
(§  64,  Ex.),  Friday,  Nov.  12,  1909.  What  was  its  standard  time 
of  southing  at  Lawrence,  Kan.?  What,  at  Denver,  Colo.? 

Since  the  times  of  this  almanac  may  for  most  purposes  be 
treated  as  local  for  the  states  named  at  the  top  of  the  calendar 
pages  (§  24),  the  requirement  is,  in  fact,  to  reduce  local  to  stan- 
dard time.  But  at  Lawrence,  10h  Om  local  time  equals  10h  21m 
standard  time,  the  standard  meridian  being  21m  east  of  the 
place.  For  Denver,  no  change  at  all  is  needed,  as  the  standard 
and  local  meridians  of  the  place  differ  only  12  seconds  (Appen- 
dix), and  so  within  that  limit,  local  agrees  with  standard  time. 

To  illustrate  the  two  steps  required  in  deriving  standard  from 
apparent  time,  the  following  example  is  added: 

EXAMPLE  5. — Required  the  clock  time  of  sun  noon  at  Columbia, 
Mo.,  Oct.  10,  1908,  the  clock  being  set  to  central  standard  time. 

41 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

Sun  noon  is,  of  course,  12h  solar  time,  and  this  like  any  other 
hour  of  apparent  time  is  reduced  to  local  mean  time  by  applying 
the  equation  of  time.  Its  value  is  given  as  13m,  under  sun  fast, 
in  Jayne's  Almanac,  so  the  Ephemeris  sign  is  minus  and  it  is  to 
be  subtracted  (§§36,  37).  The  local  mean  time  of  sun  noon  is, 
then,  llh  47m,  but  the  corresponding  standard  time  is  9m 
faster,  as  the  standard  meridian  of  Columbia  is  9m  east  of  the 
place  (Appendix).  These  steps  may  be  placed  in  tabular  form, 
as  follows : 

Sun  noon,  apparent  time,  12h   Om 

Equation  of  time,  sun  fast,  — 13 


Local  mean  time  of  sun  noon,  11  47 

Standard  meridian  east  of  Columbia,  9 


Standard,  i.  e.,  clock  T.  of  sun  noon,  11  56  A.  M. 

The  subject  of  time  is  a  difficult  one,  and  clock  dials  with 
hands  that  can  be  turned  are  helpful  in  gaining  clear  ideas 
(Byrd,  §  34). 

39.  Plotting  on  star-maps. — Any  celestial  object,  which  has 
been  definitely  placed  in  the  heavens,  in  regard  to  neighboring 
stars,  can  be  located  on  a  star-map,  and  its  coordinates  in  right 
ascension  and  declination  read  from  the  usual  reference  circles 
(§  21).  Sometimes  its  place  is  found  as  accurately  as  required 
by  mere  inspection,  and  there  are  other  observations  that  require 
but  little  more. 

EXERCISE  1. — From  the  data  given  in  the  observation  of  §  46 
find  from  " Young's  Uranography,"  first,  in  what  constellation 
the  moon  was  located;  second,  near  what  stars. 

To  answer  the  first  question,  nothing  is  needed  but  to  look  on 
Map  II,  and  note  by  the  eye  that  the  prolonged  star-line  ends  in 
Gemini.  To  answer  the  second,  mark  off  on  a  strip  of  rectangular 
paper  two-thirds  the  distance  between  a  Orionis  and  7  Gemino- 
rum,  then  pass  the  strip  through  the  stars,  so  that  the  marked 

42 


PLOTTING  ON  STAR-MAPS 

space  lies  just  above  7,  and  the  point  fixed  by  its  upper  end 
shows  that  the  moon  was  about  midway  between  £  and  d  Gem- 
inorum  but  a  little  farther  north. 

EXERCISE  2. — -As  an  illustration  of  more  critical  plotting,  let  it 
be  required  to  read  from  "Proctor's  New  Star  Atlas"  the  co- 
ordinates of  Mars,  when  the  planet  was  observed  at  the  inter- 
section of  the  diagonals  cr£  and  T$  in  the  bowl  of  "the  milk 
dipper"  (§-  59,  Obs.  1). 

Two  narrow  strips  of  rectangular  paper,  serving  for  these 
diagonals,  fix  the  place  of  the  planet  on  Map  9  of  Proctor's 
Atlas;  and  show  at  once  that  its  right  ascension  is  between 
18h  40m  and  19h  Om,  as  the  hour-circles  on  this  map  are  sepa- 
rated by  20m.  The  space  corresponding  to  20m,  marked  on 
rectangular  paper,  is  15.3  divisions,  and  the  distance  of  the 
planet  east  of  the  hour-circle,  18h  40m,  is  found  to  be  7.6d.,  d 
standing  for  divisions;  so  the  required  minutes  beyond  the 
hour-circle  are  ^|  of  20m  or  10m,  making  the  entire  right  ascension 
18h  50m. 

In  like  manner  it  is  seen  that  the  planet  is  i^  of  5°,  or 
2°. 5  below  the  parallel  of  25°,  south  declination,  so  the  whole 
decimation  is,  —  27°.5. 

In  spite  of  the  fact  that  the  planet  is  rather  unfavorably 
placed  near  the  side  of  the  map,  these  coordinates  agree  closely 
with  those  obtained  from  the  celestial  globe  (§  59,  Table). 

A  problem  in  plotting,  just  opposite  to  that  considered,  arises 
when  accurate  coordinates  of  a  heavenly  body  are  known,  and 
it  is  required  to  find  its  place  among  the  stars  on  a  map.  The 
former  process  is  then  reversed,  and  minutes  and  degrees,  that 
cannot  be  read  directly  from  the  map,  are  expressed  in  divisions 
of  rectangular  paper. 

EXERCISE  3. — The  position  of  Halley's  Comet  at  8h.5  P.  M., 
c.  s.  T.,  May  23,  1910  was,  R.  A.,  8h  4m,  and  DeeL,  +  11°.2 
(§  50,  Ex.  3).  Required  to  locate  the  comet  among  the  stars  on 
Proctor's  Atlas,  and  then  fix  its  place  critically  in  regard  to  the 
reference  circles. 

43 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

From  Map  6,  it  is  seen  directly  that  the  comet  was  nearly  in 
line  with  Procyon  and  5  Cancri,  and  about  midway  between  them. 
To  place  it  more  critically,  note  that  on  this  part  of  the  map, 

20m  =  17.0d,  and5°  =  17.5d. 

/.  A  of  17.0d  =  3.4d,  and  -^  of  17.5d  =  4.2d. 

So  the  comet  was  3.4d  east  of  the  8b-circle,  and  4.2d  north  of 
the  10°-parallel  of  north  declination. 

Star-maps  are  convenient  for  plotting,  and  the  best  of  them, 
though  far  less  expensive  than  a  celestial  globe,  are  made  with 
great  care  and  exactness.  But  errors  from  projection  are 
inevitable  ("Young's  Uranography,"  Art.  2),  and  the  globe  has 
the  advantage  of  representing  the  heavens  on  a  spherical  surface 
(§  26). 

40.  Celestial  globe  oriented. — If,  as  is  usual,  the  orientation  is 
required  for  standard  time,  five  steps  are  necessary. 

First,  the  globe  is  oriented  to  show  the  aspect  of  the  heavens, 
at  any  place  north  of  the  equator,  by  raising  the  pole  (§  15,  14) 
above  the  horizon  plate  till  its  altitude  equals  the  latitude  of  the 
place,  as  shown  on  the  meridian  ring. 

Second,  the  globe  is  adjusted  for  the  aspect  of  apparent  noon 
by  bringing  to  the  graduated  side  of  the  ring  the  sun's  place  for 
the  day  (§26). 

Third,  it  is  adjusted  for  the  aspect  of  mean  noon  by  taking 
account  of  the  equation  of  time.  When,  for  example,  that  is 
-14m,  the  mean  time  of  sun  noon  is  Ilh46m  (§  38,  Ex.  5),  but 
the  mean  time  of  mean  noon  is,  of  course,  12hOm;  so  sun  noon 
comes  before  mean  noon,  and  to  pass  from  the  former  to  the 
latter,  the  globe  must  be  turned  forward  14m,  as  read  on  the 
celestial  equator.  If  the  sign  of  this  equation  is  plus,  the  globe 
is,  of  course,  turned  backward,  i.  e.,  to  the  east. 

Fourth,  the  globe  is  oriented  for  standard  noon  by  taking 
account  of  the  difference  between  local  and  standard  meridians. 
As  an  illustration,  assume  that  the  standard  meridian  is  21m 
east  of  the  place,  then  local  noon  comes  21m  after  standard  noon, 

44 


CELESTIAL  GLOBE  ORIENTED 

and  to  pass  from  the  former  to  the  latter,  the  globe  is  turned 
21m  to  the  east.  If  the  meridian  is  west  of  the  place  the  globe  is 
turned  west. 

Fifth,  to  show  how  the  heavens  appear  at  any  hour  before  or 
after  standard  noon,  turn  the  globe  the  given  number  of  hours 
and  minutes  west  or  east  from  the  noon  position,  according  as 
afternoon  or  morning  hours  are  required. 

For  the  most  critical  adjustment,  it  is  necessary  to  plot  the 
sun's  place  from  the  Ephemeris  (§  34,  §  51,  Ex.  2),  and  to  take 
account  of  the  difference  between  the  hours  of  mean  time  and  the 
sidereal  time,  marked  on  the  celestial  equator  (§  64). 

To  aid  in  testing  the  orientation,  and  to  obtain  an  independent 
check  from  a  sidereal  time-piece,  the  right  ascension  of  the  me- 
ridian (§  49)  may  be  read  in  connection  with  all  except  the  first  of 
the  preceding  steps.  Note  that  this  right  ascension  increases  as 
the  globe  is  turned  to  the  west,  but  decreases  when  it  is  turned  east. 

EXERCISE. — Required  to  orient  the  celestial  globe  for  8h  23m 
p.  M.,  c.  s.  T.  (§  23),  Oct.  14,  1907,  Lawrence,  Kan. 

R.  A.  of  meridian  at  apparent  noon,  1       »h    rm 

from  plotted  position  of  the  sun,  f 

Equation  of  time,  p.  406  Ephemeris,  or  \  .  . 

sun  fast,  p.  21  Jayne's  Almanac,  / 


R.  A.  of  meridian  at  local  mean  noon,  13  29 

Standard  meridian  east  of  Lawrence,  21 


R.  A.  of  meridian  at  standard  noon,  13     8 

Required  interval  after  standard  noon,  8   23 

Corr.  to  reduce  8h  23m  to  sid.  interval,  1 


R.  A.  of  M.  at  8h  23m,  p.  M.,  c.  s.  T.,  21  32 

The  final  right  ascension  read  from  the  globe  should  agree 
approximately  with  correct  sidereal  time  at  8h  23m  p.  M.,  c.  s.  T., 
the  time  for  which  the  globe  is  oriented  (Byrd,  §  69). 

45 


CHAPTER^  iv. 

SUN'S  APPARENT  MOTION;  LATITUDE  FROM  SUN'S  ALTITUDE;  FIRST 
OBSERVATIONS  OP  THE  MOON;  GREENWICH  TIME;  SIDEREAL  TIME;  IN- 
TERPOLATING; PLOTTING  ON  GLOBE;  FIRST  TESTS  FOR  OPERA-GLASSES 
AND  SMALL  TELESCOPE. 

41.  Apparent  motion  of  sun  among  the  stars. — The  direction 
in  which  the  sun  seems  to  move  on  the  celestial  sphere,  and  its 
approximate  rate  can  be  determined  by  the  unaided  eye.  The 
critical  part  lies  in  connecting  sun  and  stars,  as  both  are  not 
visible  at  the  same  time.  This  may  be  effected  by  fixing  the 
point  where  the  sun  sets  by  reference,  first  to  terrestrial  objects, 
and  later,  on  the  same  evening,  from  exactly  the  same  place, 
locating  this  point  in  regard  to  the  stars,  by  the  usual  alignments. 

A  good  view  of  the  western  horizon  is  important,  and  it  is 
desirable  to  become  familiar  beforehand  with  the  constellations 
appearing  first  in  the  vicinity  of  the  sunset  point,  so  that  on  the 
evening  of  observing,  the  few  isolated  stars  that  come  first  out 
of  the  twilight  can  be  positively  identified. 

OBSERVATION. — Second-story  porch,  facing  west,  519  Oak- 
land Avenue,  Pasadena,  Calif.,  5h  P.  M.,  P.  s.  T.  (§  23),  Mon- 
day, Oct.  25,  1909.  Standing  by  the  first  awning  rod,  I  mark 
the  sunset  point  in  regard  to  distant  trees;  and  a  little  before 
six  from  the  same  position,  I  begin  looking  for  reference  stars. 
At  6  o'clock  the  following  estimates  are  made : 

1.  The  line  through  /3  Hercules  and  a  Serpentis  prolonged  its 
own  length  below  a  meets  the  horizon  5°  north  of  the  sunset 
point. 

2.  Sighting  along  the  edge  of  the  upright  awning  rod,  I  make 
the  stars  a  Herculis,  8  Opiuchi,  and  the  sunset  point  in  the  same 
straight  line.      I  estimate  also  that  the  line  through  a  and  d 
prolonged  J  its  length  meets  the  sunset  point.  (L.  B.) 

About  a  month  later,  Dec.  1,  the  sunset  point  was  located 

46 


SUN'S  MOTION  AMONG  THE  STARS 

in  like  manner  by  the  same  observer,  from  the  same  place. 
The  two  points  fixed  among  the  stars,  when  plotted  on  the  celes- 
tial globe,  show  that  o  Librae  was  setting  an  hour  later  than  the 
sun,  Oct.  25,  at  approximately  the  same  place;  and  that  on  Dec. 
1,  c  Ophiuchi  was  close  to  the  sunset  point  an  hour  after  the  sun. 
The  distance  between  the  stars,  or  to  be  exact,  the  points  near 
them,  is  found  to  measure  32°.  (L.  B.) 

In  drawing  conclusions  from  the  data  thus  obtained,  the  stars 
are  to  be  taken  as  fixed  reference  points;  and,  since  on  Dec.  1,  c 
Ophiuchi  though  about  30°  east  of  o  Librae,  was  setting  at  the 
same  interval  after  the  sun  as  o  in  October,  it  is  evident  that  the 
sun  has  meanwhile  been  moving  eastward  among  the  stars. 
And,  furthermore,  since  the  stars  were  found  at  the  sunset 
point,  when  practically  at  the  same  distance  from  the  sun,  the 
space  between  them,  32°,  gives  a  measure  of  the  sun's  motion 
during  the  interval  of  37  days  between  the  observations.  This 
makes  the  sun's  daily  rate  of  motion  0°.87  instead  of  0°.99  as 
given  by  dividing  360°  by  the  number  of  days  in  a  year,  but  it  is 
as  close  an  agreement  as  the  method  warrants,  i.  e.,-  renders 
trustworthy.  For  a  more  accurate  determination  of  rate,  see 
the  observation  of  §  63. 

42.  Sun's  bright  image  under  trees. — Sunlight  passing  through 
the  interstices  of  'leaves  forms  many  images  of  the  sun.  A  few 
are  bright  and  well  defined,  others  are  comparatively  dim;  and 
overlapping,  distorted  forms  are  not  uncommon.  Doubtless,  the 
most  interesting  time  for  observation  is  during  a  partial  solar 
eclipse,  but  on  any  day  when  the  sun  is  shining  there  is  an  oppor- 
tunity to  examine  such  images.  Let  them  fall  on  white  card- 
board, and  note  whether  varying  its  distance  and  angle  changes 
their  shape  or  size.  Observe  also  the  effect  of  different  kinds  of 
foliage,  including  shrubs  as  well  as  trees. 

To  test  whether  or  not  the  form  of  the  image  depends  upon 
the  shape  of  the  openings,  sunlight  should  be  allowed  to  pass 
through  irregular  apertures  cut  in  paper,  and  held  at  some  dis- 
tance from  the  card  on  which  the  images  fall. 

47 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

43.  Sun's  noon  altitude  from  the  gnomon. — If  the  common 
gnomon  is  used  (§5),  the  actual  observation  consists  simply  in 
marking  the  end  of  the  shadow  at  the  instant  of  apparent  noon; 
but,  since  it  is  not  easy  to  decide  exactly  where  that  comes,  it 
is  desirable  to  bring  out  the  north  part  of  the  shadow  sharply 
by  letting  it  fall  on  white  paper.  The  mark  for  the  end  is,  per- 
haps, best  placed  midway  between  the  dark  part  of  the  shadow 
and  the  outer  edge  of  its  penumbra.  Final  results  depend  largely 
upon  using  a  true  upright,  well  adjusted. 

In  making  measures,  be  careful  to  get  the  whole  length  of  the 
shadow,  which,  if  a  gnomon  box  is  used,  includes  the  width  of 
its  frame,  and  sometimes  a  little  space  besides,  depending  upon 
adjustment.  Often,  too,  the  height  of  the  gnomon  includes  a 
part  of  the  height  of  the  box. 

OBSERVATION  1. — Wide  View,  near  Lawrence,  Kansas,  Satur- 
day, Dec.  22,  day  of  the  winter  solstice,  1906.  Gnomon  post  No. 
1  is  adjusted  in  the  gnomon  box  on  the  roof  platform,  and  the 
end  of  its  shadow  marked  within  a  minute  of  sun  noon;  for,  dur- 
ing more  than  that  interval,  the  length  of  the  shadow  does  not 
change  perceptibly. 

Three  independent  measures  made  of  each,  give  the  length  of 
the  shadow  57.06  in.,  and  the  height  of  the  gnomon  30.00  in. 
From  these  values,  altitude  is  derived,  as  explained  in  §  31,  the 
angle  read  from  a  large  protractor  being  27°.8,  and  that  derived 
from  calculation,  27°  44'.  In  like  manner,  on  the  day  of  the 
summer  solstice  June  22,  1907,  the  sun  was  observed  at  noon,  at 
the  same  place,  and  its  altitude  from  the  protractor  found  to  be 
74°.7,  from  calculation  74°  40'. 

When,  as  here,  the  determination  of  altitude  is  carried  to  min- 
utes, the  correction  for  refraction  should  be  included  (Young, 
Art.  50),  if  it  amounts  to  a  minute  or  more.  Reference  to  a  table 
of  mean  refractions  ("Young's  Manual  of  Astronomy,"  Table 
VIII)  shows  that  2'  is  to  be  substracted  from  the  first  altitude, 
making  it  27°  42',  but  for  the  second  no  change  is  needed. 

The  section  of  a  sheltered  plumb  line  may  serve  as  a  gnomon, 
though  the  required  measurements  are  not  so  readily  effected. 

48 


LATITUDE  FROM  SUN'S  ALTITUDE 

OBSERVATION  2. — W.  V.  Lawrence,  Kansas,  Tuesday,  March 
19,  1912.  To  employ  as  a  gnomon  the  plumb  line  near  the 
south  opening  of  the  plumb-line  booth  (§  9),  a  section  is  marked 
off  by  a  bead  fixed  on  the  line  a  few  inches  below  its  supporting 
hook. 

Since  the  floor  of  this  temporary  booth  is  somewhat  uneven,  a 
smooth,  heavy  plank,  is  laid  down  under  the  plumb  lines  and 
carefully  levelled.  White  paper  is  pasted  on  the  north  end,  and 
when  the  meridian  line,  marked  upon  it,  bisects  the  shadow  of  the 
bead,  a  short  line  is  drawn  east  and  west  through  its  center. 

In  this  observation,  the  height  of  the  '  'gnomon7 '  is  the  distance 
from  the  centre  of  the  bead  to  the  point  of  the  plumb  bob,  or 
rather,  to  the  mark  a  few  hundredths  of  an  inch  below  it;  and 
the  length  of  its  shadow  is  the  distance  from  this  mark  to  the 
east  and  west  mark  on  the  meridian  line.  The  mean  of  several 
measures,  for  each,  makes  the  former  52.64  in.,  the  latter  43.12 
in.,  and  the  sun's  altitude  derived,  as  usual,  is  50°  40'. 

44.  Latitude  from  sun's  noon  altitude. — The  main  object  in 
determining  the  altitude  of  the  sun  on  the  dates  of  the  equinoxes 
and  the  solstices  is  to  obtain  data  for  finding  latitude.  For  the 
sun's  noon  altitude  at  either  equinox  gives  latitude,  independ- 
ently of  declination  (Byrd,  §  115);  and  this  is  also  true  of  the 
combined  altitudes  at  the  solstices,  provided  it  is  regarded  as  a 
known  fact,  that  the  sun,  at  these  times,  reaches  points  equally 
distant,  north  and  south  of  the  equator. 

EXERCISE  1. — From  the  noon  altitude  of  the  sun  at  the  sol- 
stices, derived  in  Obs.  1  of  the  preceding  section,  required  to 
find  the  latitude  of  the  given  station. 

Let  SS'  and  SS",  in  Fig.  8  (§  27,  Fig.  4),  on  page  51,  represent 
the  observed  altitudes.  The  corresponding  zenith  distances  are 
then  S'Z  and  S"Z,  and  their  mean  is  equal  to  QZ,  since,  as  just 
stated,  QS'=QS";  but  QZ  is  the  declination  of  the  zenith,  which 
equals  the  latitude  (§27).  Therefore,  half  the  sum  of  the  sun's 
zenith  distances,  determined  at  noon  on  the  days  of  the  solstices, 
equals  the  latitude  of  the  place. 

49 

4 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

If  the  numerical  values  for  zenith  distances  are  substituted, 
£"Z  =  62°  18',  S'Z  =  15°  20'  (§  43,  Obs.  1);  and  the  mean  of  the 
two,  38°  49',  gives  a  value  for  the  latitude  of  Wide  View.  As  a 
check,  it  may  be  noted  that  the  latitude  of  the  State  University, 
several  miles  east,  but  less  than  a  mile  north,  is  given  as  38°  57' 
(§  8?;  Ex.  1). 

The  obliquity  of  the  ecliptic  QS'  or  QS"  (§  15,  28}  derived  from 
these  zenith  distances,  is  23°  29',  showing  a  closeness  of  agree- 
ment with  the  Ephemeris  value,  23°  27',  which  is  doubtless  due 
in  part  to  accident. 

If  the  sun's  declination  is  obtained  from  an  almanac  (§§25,  34), 
any  noon  altitude  may  be  employed  to  find  latitude. 

EXERCISE  2. — From  the  sun's  noon  altitude  for  March  19, 
given  in  Obs.  2  of  the  preceding  section,  find  the  latitude  of  Wide 
View. 

Since  this  is  the  day  before  the  spring  equinox,  the  sun  is  just 
a  little  below  Q,  Figure  8,  say  at  Si.  Its  zenith  distance  is  then, 
Si  Z,  its  declination  QSi,  and  the  difference  in  the  two  gives  QZ, 
the  declination  of  the  zenith,  or  the  latitude  required.  The 
numerical  reduction  may  be  arranged  thus : 

Sun's  observed  altitude,  50°       40' 

Correction  for  refraction,  1 

Corrected  altitude,  50        39 

Sun's  zenith  distance,  39        21 

Sun's  decl.  fr.  p.  10,  O.  F.  A.,  -30 


Decl.  of  zenith  or  latitude,  38        51 

True  latitude  of  Wide  View,  38        57 


Error  of  observation,  6 

The  declination  is  so  small  that,  if  no  account  is  taken  of  it, 
the  latitude  still  comes  within  half  a  degree  of  the  correct  value. 
(§  2,  Ex.  25). 

50 


LATITUDE  FROM  SUN'S  ALTITUDE 

Another  determination  made  a  few  days  later  in  the  same  way, 
at  the  same  place  gave  a  latitude  of  38°  55'.     (See  Ex.  3.) 


FIG.  8. 

EXERCISE  3. — From  the  data  given  in  the  observation  of  §  31, 
find  the  latitude  of  Normal  College,  New  York,  N.  Y. 

Reference  to  the  given  section  shows  that  on  May  29,  1913, 
the  sun  was  observed  from  the  window  gnomon,  and  its  image 
bisected  a  little  before  noon.  Measures  made  of  the  vertical 
distance  from  the  center  of  the  aperture  to  the  south  point  of 
the  meridian  line,  and  the  distance  of  the  latter  point  to  the 
center  of  the  image,  gave  respectively,  20.00  in.  and  6.94  in. 
(Fig.  6,  §  31).  If  then,  z  is  the  sun's  zenith  distance, 

ft  Q4. 

tan  2  =  -B±?  and  z  =  19°  8'. 
20.00 

Refraction,  as  it  is  less  than  half  a  minute  is  not  included; 
and  since  for  this  date  the  declination  of  the  sun  is,  +21°  36',  the 
declination  of  the  zenith,  that  is  the  latitude  of  the  place  is, 
19°  8'+21°  36',  i.  e.,  40°  44'.  As  the  true  latitude  of  the  college 
is  40°  46'  (Appendix),  the  error  is  2',  an  error  which  is,  however, 
too  small  to  be  considered  trustworthy,  especially  as  the  latitude 
derived,  in  like  manner,  on  the  same  day  by  another  observer 
was  in  error  12'. 

Since  south  declinations  are  negative  (§  15,  28),  the  general 
rule  for  finding  latitude  from  the  sun's  zenith  distance  is,  add 
algebraically  to  that  distance,  the  sun's  declination  for  the  given 
date. 

51 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

45.  First  observations  of  the  moon. — Look  first  for  the  new 
moon  the  evening  after  it  is  set  down  as  new  in  the  almanac. 
Under  favorable  conditions,  it  is  possible  to  see  it  then,*  and  the 
following  evening  it  ought  to  be  found,  if  the  sky  is  clear. 

After  sunset  has  been  observed,  and  its  time  and  place  noted 
approximately  (§  18),  the  search  for  the  moon  should  begin. 
When  it  is  first  visible,  record  the  time  within  a  few  minutes,  note 
in  what  direction  the  horns  point,  what  angle  the  line  joining 
them  makes  with  the  horizon  (Byrd,  §  142),  and  whether  the  dark 
and  illuminated  parts  seem  to  belong  to  the  same  circle.  Watch 
the  moon  also  at  setting,  entering  in  the  notes  the  hour  and 
minute,  and  locating  the  point  where  it  disappears,  either  by 
sketching  a  small  section  of  the  horizon,  or  measuring  azimuth 
or  amplitude  (§  15,  12,  13).  The  observation  should  give  data 
for  describing  the  appearance  known  as  the  "old  moon  in  the 
new  moon's  arms/'  for  comparing  the  actual  time  of  setting  with 
the  almanac  time,  and  also  the  time  and  place  of  the  setting  of 
the  sun  and  moon  on  the  same  date. 

46.  Moon  placed  in  constellation. — To  find  out  about   the 
motion  of  the  moon,  it  is  necessary  to  locate  it  a  number  of  times 
among  the  stars,  so  the  question  often  to  be  answered  is,  "In 
what  constellation  is  the  moon  tonight?"     In  fixing  its  place, 
depend  directly  upon  the  eyes,  drawing  imaginary  star-lines,  and 
estimating  distances  and  angles,  as  in  mapping  a  constellation 
(§  33).     It  is,  however,  desirable  to   place  the  moon,  or  any 
moving  body,  at  the  end  of  one  side  of  an  angle,  rather  than  at 
its  vertex,  i.  e.,  Z  ay  Ceti  2>  =90°  (§  57,  Obs.),  not   Z SO) 0  =  90°. 

The  main  difficulty  in  locating  the  moon  lies  in  the  fact  that 
its  own  light,  as  well  as  twilight,  puts  out  the  fainter  stars,  and 
obliterates  the  characteristic  features  of  neighboring  constella- 
tions, so  that  it  is  not  easy  to  see  and  identify  comparison  stars. 
For  the  new  moon  it  is  helpful  to  become  familiar  beforehand 
with  the  appearance  of  the  sky  near  the  western  horizon  in  the 

*  "Denning's  Telescopic  Work  for  Starlight  Evenings,"  p.  136. 

52 


MOON'S  SYNODIC  PERIOD 

early  evening  (§  41);  but  when  this  is  impracticable,  reference 
should  be  made  to  star-maps  or  the  celestial  globe,  properly  ori- 
ented (§  40).  A  slow-moving  bright  planet  which  has  been  fol- 
lowed from  week  to  week,  and  is  known  to  be  in  the  vicinity  of 
certain  stars,  serves  at  times  to  fix  the  constellation;  and  it  is 
always  admissible  to  use  opera-glasses,  if  the  fact  is  stated 
(§  17,  3).  When  sunlight  interferes,  or  clouds  blot  out  all  celes- 
tial objects  except  the  moon,  its  place  may  be  found  by  measuring 
its  altitude  and  azimuth,  and  later  plotting  these  coordinates  on 
the  celestial  globe  (§  51,  Ex.  1). 

The  location  of  the  moon,  when  it  is  favorably  placed,  in  line 
with  two  stars  (§  33)  is  illustrated  as  follows: 

OBSERVATION. — 84  Elm  Street,  Northampton,  Mass.  7h  p.  M., 
E.  s.  T.,  Wednesday,  March  11,  1908.  The  moon  is  in  line  with 
a  Orionis  and  7  Geminorum,  and,  if  this  star-line  is  prolonged 
upward  f  of  its  own  length,  it  reaches  the  moon.  (A.  E.  T.) 

From  globe  or  map  it  is  seen  by  mere  inspection  that  the  moon 
was  in  Gemini,  and  plotting  fixes  its  place  near  the  stars  £  and  6 
(§  39,  Ex.  1). 

For  a  more  critical  location  of  the  moon  in  reference  to  the 
stars  see  §  57,  Ex. 

47.  Moon's  synodic  period. — This  period  is  the  interval  from 
new  moon  to  new  moon,  or  from  any  phase  to  the  same  phase 
again.  To  determine  its  length,  drawings  may  be  made  of  the 
moon  in  different  lunations.  (See  also  Byrd,  §  143). 

OBSERVATION. — S.  C.  0.,  Northampton,  Mass.  In  order  to 
find  the  length  of  the  synodic  period,  I  have  made  this  fall,  1911, 
five  naked-eye  sketches  of  the  moon,  outlining  carefully  the 
terminator  and  the  markings  visible.  Later,  comparison  shows 
that  those  obtained  Oct.  2nd  and  30th  are  quite  similar,  though 
in  the  first,  the  terminator  is  slightly  convex,  while  in  the  second, 
the  moon  appears  just  about  half  full.  My  next  observation  was 
on  Nov.  2,  and  by  noting  the  rate  of  change  between  that  date 
and  Oct.  30,  I  estimate  that  it  would  take  1.5  days  for  the  moon 
to  pass  from  the  phase  seen  Oct.  30  to  that  of  Nov.  2.  The  syno- 

53 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

die  period  required  is,  therefore,  the  interval  between  these  dates, 
28  days,  plus  1.5  days  or  29.5  days. 

The  same  result  is  obtained  by  comparing,  in  like  manner, 
the  sketches  of  Nov.  2  and  Dec.  4.  The  corresponding  Ephe- 
meris  intervals  are,  29d  20h  and  29d  llh.  (H.  P.  O'M.) 

48.  Greenwich  time  changed  to  local  or  standard  time,  and 
vice  versa. — These  reductions  are  similar  to  those    already    de- 
scribed (§  38),  and  the  same  principle  applies,  that  is,  the  time  of 
one  meridian  is  expressed  in  that  of  another  by  making  a  correc- 
tion for  the  difference  in  longitude  between  them.     Since  in  our 
country  all  longitudes   are  reckoned  west  from  Greenwich,  the 
following  precepts  apply: 

When  Greenwich  time  is  given,  and  local  or  standard  time 
required,  subtract  from  the  former  the  difference  in  longitude 
between  the  two  meridians  employed;  but  add  this  difference  to 
local  or  standard  time  in  order  to  find  the  corresponding  Green- 
wich time. 

EXAMPLE. — Find  the  Greenwich  time  corresponding  to  llh 
45m  A.  M.,  local  time  at  Salt  Lake  City;  corresponding  to  llh 
45m  A.  M.,  standard  time  at  Salt  Lake  City. 

The  longitude  of  this  place  is  7h  28m  W.  (Appendix),  or,  in 
other  words,  that  is  the  difference  in  longitude  between  the 
meridians  of  Greenwich  and  Salt  Lake  City.  It  is,  then,  the 
interval  of  time  to  add  to  the  given  local  time,  llh  45m  A.  M., 
to  obtain  the  corresponding  Greenwich  time,  7h  13m. 

But  the  longitude  of  Salt  Lake's  standard  meridian  is  7h  W., 
so  that  number  of  hours  added  to  the  given  standard  time, 
llh  45m  A.  M.,  gives  6h  45m,  as  the  Greenwich  time  required. 
Neither  here  nor  above  are  the  letters  p.  M.  added,  for  Green- 
wich time  is  usually  expressed  as  astronomical  time  (§  35). 

49.  Sidereal  time  and  right  ascension  of  the  meridian. — The 

instant  when  the  vernal  equinox  (§15,  26)  crosses  the  local  meri- 
dian, fixes  sidereal  noon,  and  its  hour-angle  at  any  moment  is 
sidereal  time.  But  this  hour-angle  equals  the  arc  on  the  celestial 

54 


INTERPOLATING 

equator  intercepted  between  the  foot  of  the  meridan  and  the 
vernal  equinox  (§  15,  2Jf),  an  arc  which  also  measures  the  right 
ascension  of  an  object  when  it  is  on  the  meridian  (§  15,  29). 
So  it  follows  that  the  sidereal  time  of  a  star's  meridian  transit 
equals  its  right  ascension. 

Since  it  is  customary  to  speak  of  the  right  ascension  of  the 
meridian,  just  as  of  an  object  on  the  meridian,  its  right  ascension 
is  said  to  be  sidereal  time;  and  when  the  globe  is  oriented  for  any 
position,  the  right  ascension  of  the  meridian,  read  at  the  grad- 
uated side  of  the  meridian  ring,  is  the  sidereal  time  corresponding 
to  that  particular  aspect  of  the  globe  (§  40,  Ex.). 

50.  Interpolating  between  almanac  values. — Much  of  the 
astronomical  data  given  in  almanacs  depends  upon  the  element 
of  time;  and,  for  naked-eye  observing,  it  is  usually  accurate 
enough  to  treat  the  required  functions  as  varying  directly  with 
the  time.  The  following  exercises  illustrate  interpolations  re- 
quired in  preceding  or  following  sections : 

EXAMPLE  1. — Two  consecutive  times  for  the  setting  of  Saturn, 
given  in  Jayne's  Almanac,  1910,  are, 

Feb.  22,          9h     30m,  p.  M. 
March  22,      7      57,    p.  M. 

Required  the  approximate  time  of  the  planet's  setting,  Feb.  25. 

The  change  in  the  time  of  setting  is  93  minutes  in  28  days,  and 
so  for  the  three  days,  between  the  22d  and  25th,  the  change  is 
taken  as  A,  i.  e.,  J,  of  93m  or  10m.  Therefore,  for  Feb.  25, 
the  almanac  time  of  setting  is  9h  30m— 10m,  or  9h  20m  p.  M. 
(§  32,  Obs.). 

EXAMPLE  2. — The  right  ascension  and  declination  of  the  moon 
were  determined  by  the  unaided  eye  at  Mantoloking,  N.  J.,  3h  35m 
A.  M.,  E.  s.  T.,  Tuesday,  July  21,  1908  (§  57,  Obs.).  Required 
the  coordinates  from  the  Ephemeris  for  this  time. 

Since  the  values  sought  are  to  be  found  in  the  Greenwich  sec- 
tion of  the  Ephemeris  (§  34),  the  time  of  observation  must  first 
be  expressed  in  the  time  used  there.  According  to  §  35,  the 

55 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

astronomical  date  is  15h  35m,  July  20,  and  by  §  48,  the  Green- 
wich time  is  5h  hours  later  or  20h  35m,  so  the  coordinates  are 
to  be  taken  out  for  a  time  Oh.4  before  21h,  as  it  is  the  rule  in 
interpolating,  to  work  always  from  the  function  nearest  that 
required.  The  moon's  right  ascension  and  declination  for  20 
and  21  hours,  from  p.  118  of  the  Ephemeris  are, 

July  20,  20h,  0>'s  R.  A.,  2h  30m;  3's  Decl.,  +  10°.2 
"    21,    OTsR.  A.,  2  32   ;  0>'s  Decl.,  +  10.4 

In  one  hour,  therefore,  the  change  in  R.  A.  is  2m,  and 
in  Decl.,  0°.2,  and  0.4  of  these  differences  subtracted  from 
the  values  opposite  21h,  gives  the  required  coordinates  of  the 
moon, 

July  20,  20b  35m,  R.  A.,  &  31m;  and  Decl.,  +  10°.3 

EXERCISE  3. — The  following  positions  for  Halley's  Comet,  1910, 
are  taken  from  Dr.  Smart's  Ephemeris,  computed  for  9h  Green- 
wich time.  (Journal,  British  Ast.  Ass.,  Vol.  XX,  No.  6): 

May  23,  R.  A.,  7h  58m.O;  Decl., +  11°  40' 
May  24,  R.  A.,  8   26  .4;  Decl.,  +  9    33 

Required  the  coordinates  of  the  comet  at  8h.5  P.  M.,  c.  s.  T., 
May  23,  1910. 

The  time,  8h.5  p.  M.,  for  which  the  coordinates  are  desired, 
equals  14h.5,  Greenwich  time  (§  48),  and  so  is  5h.5  later  than  that 
for  which  the  Ephemeris  is  given.  Since  the  change  in  right 
ascension  in  24h  is  28m.4,  and  in  Decl.  2°  7',  'M  of  these  dif- 
ferences are  to  be  combined  with  the  Ephemeris  values  for  May 
23,  fixing  the  comet's  place  in, 

R.  A.,  8h  4m.5,  and  Decl.,-f-H°  11'. 

When  final  results  are  to  be  carried  only  to  the  nearest  minute 
of  time  and  tenth  of  a  degree  of  arc,  a  difference  of  several  hours 
often  makes  no  change  in  the  Ephemeris  value. 

EXERCISE  4. — Find  the  right  ascension  and  declination  of  Mer- 
cury for  8h  4m,  p.  M.,  c.  s.  T.,  April  19,  1911,  at  a  place  in 
longitude  6h  21m  W.  and  latitude  +39°.0. 

56 


PLOTTING  ON  CELESTIAL  GLOBE 
Washington  time  is  first  obtained  as  follows : 

Central  standard  time,  8h         4E 

Standard  meridian  east  of  place,  21 


Local  mean  time,  7        43 

Washington  east  of  place,  1         13 


Washington  time  of  observation,  8        56 

Since  the  Washington  time  for  which  the  coordinates  of  the 
planet  are  given  is  lh  8m,  it  follows  that  8h56m-lh8m  or 
7h  48m  is  the  interval  to  be  used  in  making  the  interpolation. 
During  24  hours,  the  changes  in  coordinates  are,  lm.9  in  right 
ascension  and  7'  in  decimation,  so  the  corrections  required  are 
%f  or  J  of  these  differences,  making  right  ascension  2h  55m.2 
and  declination  19°  47',  values,  which  if  taken  only  to  the  near- 
est minute,  and  tenth  of  a  degree  are  the  same  as  those 
given  directly  in  the  Ephemeris  (§  17,  9). 

After  some  practice,  interpolations  like  those  above  are  to  be 
made  wholly,  or  in  large  part  mentally. 

51.  Plotting  on  the  celestial  globe. — In  general,  plotting 
on  the  globe  closely  resembles  that  done  on  star-maps  (§  39). 
There  are,  however,  differences  in  detail,  and  where  the  object 
considered  is  referred  to  the  horizon,  it  is  practicable  to  use 
the  globe  only. 

EXERCISE  1. — The  coordinates  of  a  body  thought  to  be  Mercury 
were  measured  with  jointed-rods  and  protractor,  at  8h  4m,  p.  M., 
c.  s.  T.,  April  19,  1911,  in  longitude  6h  21m  W.,  latitude,  +39°. 
The  altitude  obtained  was  5°.5,  azimuth  112°.5  required  to  locate 
the  body  among  the  stars  and  find  out  whether  or  not  it  was 
Mercury. 

It  should  be  added  that  according  to  the  original  notes,  the 
observation  was  made  under  difficulties,  for  no  meridian  line 
was  available,  and  the  west  point  was  taken  roughly  by  aligning 

57 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

from  the  frame  of  a  west  window.     However,  no  other  object  in 
the  vicinity  was  nearly  as  bright. 

In  order  to  locate  the  body  on  the  globe,  orient  it  for  latitude 
and  time  (§  40),  and  see  that  it  is  held  firmly  in  position  (§  29). 
Then  mark  off  the  observed  altitude  5°. 5,  near  one  end  of  a  nar- 
row strip  of  paper,  which  serves  as  a  vertical  circle.  Pass  the 
other  end  through  the  zenith  point  of  the  globe  (§  27),  bringing 
the  lower  mark  for  altitude  to  coincide  with  the  given  azimuth, 
112°. 5,  as  read  on  the  horizon  plate,  and  the  upper  mark  for  alti- 
tude fixes  the  place  of  the  body  observed.  This  point  is 
marked  by  a  dot  on  a  bit  of  paper,  moistened  and  pressed  on  the 
globe.  It  is  found  to  be  in  the  constellation  Aries,  near  the  fifth 
magnitude  star  €.  To  obtain  its  coordinates  referred  to  the 
equator,  one  method  is  as  follows  (Ex.  3):  Unclamp  the  globe, 
turn  it  till  the  marked  point  comes  to  the  graduated  side  of  the 
meridian  ring,  and  the  number  of  degrees  opposite,  21°. 3,  gives 
the  required  declination;  and  the  corresponding  right  ascension 
is  the  time,  2h  51m,  read  from  the  equator  where  it  intersects 
the  ring. 

Since  the  values  taken  from  the  Ephemeris  are  R.  A.,  2h  55m 
and  Decl.  +19°.8  (§  50,  Ex.  4),  the  two  sets  of  coordinates,  taken 
in  connection  with  the  statement  about  brightness,  show  an 
agreement  close  enough  to  warrant  the  conclusion  that  the  body 
observed  was  Mercury. 

The  converse  of  this  problem  arises  when  right  ascension  and 
declination  are  known,  and  it  is  required  to  find  altitude  and 
azimuth,  either  to  check  observed  values,  or  to  make  a  setting 
with  the  altazimuth  instrument  so  as  to  pick  up  quickly  a  faint 
object.  As  an  illustration,  the  data  given  in  connection  with  the 
preceding  exercise  may  be  taken  in  reverse  order. 

EXERCISE  2. — The  right  ascension  and  declination  of  Mercury 
for  the  evening  of  April  19,  1911  are,  2h  55m  and,  +19°.8,  respec- 
tively, (§  50,  Ex.  4)  find  its  altitude  and  azimuth  for  the  time  and 
place  of  Exercise  1. 

Here  the  first  step  is  to  locate  Mercury.  Turn  the  globe,  there- 
fore, till  the  given  right  ascension,  read  on  the  equator,  comes  to 

58 


PLOTTING  ON  CELESTIAL  GLOBE 

the  graduated  side  of  the  meridian  ring,  look  along  its  edge  for 
the  number  of  degrees  in  the  declination,  and  just  opposite  is  the 
place  for  the  planet,  which  is  marked  as  in  Exercise  1. 

To  obtain  its  coordinates  referred  to  the  horizon,  orient  the 
.globe  for  time  and  place  of  observing,  clamp  it  in  position,  and 
pass  a  strip  of  paper  through  the  zenith  point  of  the  globe,  and 
that  fixed  for  Mercury.  Where  it  intersects  the  horizon  plate, 
the  reading  for  azimuth,  110°.8  is  that  required,  and  the  intercept 
between  the  planet  and  the  plate,  4°. 6  is  the  corresponding 
altitude. 

It  is  evident  that  either  one  of  these  exercises  gives  an  identi- 
fication of  the  body  observed,  and  that  is  the  main  object  of 
such  plotting,  especially  as  values  of  altitude  and  azimuth  which 
cannot  be  checked  from  declination,  or  readily  from  the  globe 
{§§  28,  29),  are  usually  tested  adequately  by  plotting  on  rectan- 
gular paper  (§  80). 

A  more  common  form  of  plotting  is  employed  in  verifying  or 
correcting  the  star  places,  and  dots  for  the  sun  (§  26),  which  are 
marked  on  the  globe. 

EXERCISE  3. — In  reducing  the  observation  of  Venus  and  Mars 
when  in  conjunction  (§60),  the  star-line  5e  Orionis,  measured,  on 
the  globe,  was  found  to  differ  a  third  of  a  degree  from  the  length 
derived  by  calculation.  Required  to  plot  these  stars  on  the  globe 
and  find  the  distance  between  the  places  thus  obtained. 

The  coordinates  of  5  Orionis,  taken  from  mean-star  places  in 
the  Ephemeris  for  1908  (§  34),  are  R.  A.,  5h  27m.3,  and  Decl., 
— 0°.37.  To  fix  its  place  as  accurately  as  possible  it  is  better, 
instead  of  using  the  meridian  ring  of  the  globe  (Ex.  l)  to  work 
directly  from  the  nearest  reference  circles,  as  on  star-maps  (§  39). 
Since,  however,  there  are  on  the  globe  no  intermediate  circles 
between  those  for  whole  hours,  and  10°-spaces,  27m.3  and  0°.37 
must  be  expressed  in  linear  measure.  On  the  equator,  near 
which  the  stars  are  situated,  it  is  seen  that  60m  =  52.4d,  d  stand- 
ing for  a  division  of  rectangular  paper  used,  and  10°  in  declina- 
tion equals  35.0d.  Therefore,  27m.3  =  il  of  52.4d,  or  23.8d, 
and  0°.37  =  .37  of  3.5d  or  1.3d;  and  the  point  for  the  star 

59 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

is  marked  23.8d  east  of  the  5h-circle  and  1.3d  south  of  the 
equator.  In  like  manner  «  Orionis  is  located  and  the  space  be- 
tween them,  5.0d,  on  the  basis  of  105d  to  30°  equals  1°.4,  a  value 
agreeing  with  that  obtained  by  trigonometry  (Byrd,  §  72).  , 

Here,  as  usual  in  numerical  calculations,  the  preliminary  work 
is  carried  further  than  final  results,  i.  e.,  one  tenth  of  a  division 
of  the  paper  is  less  than  a  tenth  of  a  degree. 

By  far  the  largest  number  of  exercises  which  require  plotting 
on  the  globe  are  connected  with  direct  observation  of  position 
for  moon,  planets,  and  comets,  where  the  data  given  are  esti- 
mates of  distance,  and  angular  direction  from  neighboring  stars. 

EXERCISE  4. — Pasadena,  Calif.,  4h.3  A.  M.,  p.  s.  T.,  Saturday, 
September  7,  1907.  The  position  of  Daniel's  Comet  was  fixed 
among  the  stars  by  the  following  estimates  (§72,  Obs.  2): 

Position  1 — Zj8a  Cancri  c£  =  175,   a  Cancri  c£  =  f  a/3  Cancri. 

Position  2 —  Z  f  Hydrae  a  Cancri  <&  =  95°,  a  Cancri  <&  =  1|  a 
Cancri  £  Hydrae. 

Required  to  locate  the  comet  on  the  globe  and  find  its  right 
ascension  and  declination. 

Adjust  the  globe  and  secure  it  in  position  with  the  constella- 
tions Cancer  and  Hydra  in  convenient  position.  Cut  out,  with 
the  help  of  a  protractor  (§11),  the  paper  forms  for  the  angles,  and 
proceed  thus  with  the  first  set  of  estimates. 

Place  the  vertex  of  the  angular  form  for  175°  on  the  star,  a 
Cancri,  with  one  side  passing  through  /3  Cancri,  and  the  other 
extending  indefinitely  in  the  direction  of  the  comet,  as  shown  by 
Fig.  10,  §  72.  Then,  on  the  latter  side,  lay  off  f  a/3,  and  the 
point  marking  the  end  of  that  space  fixes  the  first  position  of  the 
comet.  The  second  is  found  in  like  manner,  and  as  the  obser- 
ver's notes  contain  nothing  about  unequal  weighting  (Byrd,  §  4), 
the  point  midway  between  the  two  is  taken  as  the  observed  place 
for  the  comet. 

To  derive  the  coordinates  of  this  point  in  reference  to  the  equa- 
tor, it  is  to  be  noted  that  51. Od  equals  60°*  on  this  part  of  the 
globe,  and  that  35.3d  equals  10°  of  declination.  Then,  as  the  dot 
for  the  comet  is  found  to  be  23.0d  east  of  the  9h-circle,  and 

60 


FIRST  TESTS  OF  OPERA-GLASSES 

11.7d  north  of  10°-parallel,  north,  the  corrections  to  be  added  to 
the  values  read  directly  are,  f?  of  60*  or  27m;  and  gjj  of  10°  or 
3°.3,  making  the  required  right  ascension,  9h  27m,  and  declin- 
ation, +  13°.3. 

The  telescopic  position  fixed  at  Vienna,  corresponding  to  the 
time  of  this  observation  and  carried  only  to  the  same  limits  is, 
E.  A.,  9m  27s  and  Dec!.,  +11°.9  (§  72). 

When  a  series  of  observations  is  to  be  plotted,  paper  that  is 
simply  moistened  is  unsatisfactory,  as  the  pieces  are  likely  to 
drop  off  before  the  work  is  finished.  For  such  exercises,  it  is  well 
to  prepare  beforehand  narrow  strips  of  paper,  like  the  margins 
of  a  newspaper,  by  spreading  on  them  a  very  thin  layer  of  pho- 
tographer's paste  and  allowing  it  to  dry.  Plotting  is  also  facil- 
itated, if  all  angular  forms  required  are  cut  out  beforehand, 
coordinate  paper  being  preferably  used  for  the  purpose. 

To  mark  out  a  path  graphically,  after  locating  a  number  of 
points,  fine,  flexible  wire,  small  cord,  or  coarse  thread,  well  waxed 
are  serviceable,  and  bits  of  paper,  like  that  just  mentioned,  may 
be  used  to  hold  any  one  of  them  in  place  while  tests  and  com- 
parisons are  being  made.  (  §  57,  Obs.). 

52.  First  tests  of  opera-glasses. — A  good  pair  of  opera-glasses, 
when  pointed  at  the  moon,  for  example,  gives  one  field  of  view, 
one  image  and  no  fringes  of  light.  If,  however,  in  looking  at 
the  sky,  two  circles  of  light  appear,  either  distinct  or  overlapping, 
the  glasses  have  the  defect  of  double  field  of  view.  It  is  not  un- 
common and  interferes  little  with  their  use,  but  if  two  images  of 
a  single  object  are  seen,  the  instrument  is  worthless.  Conspicuous 
fringes  of  light  about  a  bright  object  are  also  objectionable,  but 
a  little  extraneous  light  does  no  harm. 

In  finding  the  diameter  of  the  object-glasses,  it  will  not  do  to 
lay  anything,  even  a  strip  of  paper,  on  the  glass  itself.  Instead, 
place  a  finely  graduated  scale  on  the  top  of  the  cell,  as  nearly 
over  the  center  as  possible,  and  align  downward  by  the  eye. 
The  mean  of  three  diameters  read  thus  is  accurate  enough  for 
all  practical  purposes. 

61 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

53.  Preliminary    exercises    with    a   telescope. — A    telescope 
should  be  used  first  in  the  daytime,  when  the  essential  parts  and 
the  connection  between  them  can  be  plainly  seen.     This  is  the 
time  to  practice  making  the  different  motions  and  adjustments,  to 
focus  on  a  distant  terrestrial   object  and  ascertain  how  the  in- 
strument inverts,  that  is,  whether  the  image  is  turned  partially, 
as  in  a  mirror,  or  whether  it  is  completely  inverted,  both    up 
for  down  and  right  for  left. 

In  focusing  either  telescope  or  opera-glasses,  pains  must  be 
taken  to  obtain  sharp,  clear-cut  images.  Never  be  satisfied  with 
motion  in  one  direction,  but  push  the  eye-piece  in  and  draw  it 
out,  till  the  point  of  most  distinct  vision  is  passed  in  opposite 
directions,  and  then  a  quick  motion  or  two  should  give  that  point. 

For  the  first  evening  exercise  three  things  are  important,  to 
repeat  with  a  bright  body,  the  moon  if  possible,  the  observations 
already  made  on  a  terrestrial  object,  to  find  in  what  direction 
heavenly  bodies  cross  the  field  of  view,  and  to  determine  how  the 
telescope,  when  carefully  focused,  affects  the  size  and  brightness 
of  stars  and  planets. 

In  handling  a  telescope,  it  is  hardly  possible  to  exercise  too  much 
care.  Hasty,  rough  motions,  pushing  hard,  or  jamming  any  of  the 
parts  are  reckoned  among  the  deadly  sins  of  an  astronomer. 

54.  Light-gathering  power  of  a  telescope. — A  telescope  brings 
to  the  eye  far  more  light  than  falls  directly  on  the  pupil,  for  that 
has  a  diameter  of  only  about  0.2  of  an  inch,  and  the  light  received 
on  different  circles  varies  as  the  square  of  their  diameters.     If 
then,  the  diameter  of  an  object-glass  is  2  inches,  and  L  and  Lf 
represent  the  quantity  of  light  falling  respectively  on  the  eye 
and  on  the  objective,  their  relative  amounts  are  given   by  the 
proportion, 

L:I/::(0.2)2:(2.0)V.  4 L  =  .04 L'  and  L'  =  100 L. 

Since,  however,  even  with  a  small  telescope,  nearly  £  of 
the  light  is  lost  in  passing  through  the  lenses,  a  telescope 
with  a  2-inch  objective  brings  to  the  eye  about  80  times  as  much 
light  as  it  receives  directly. 

62 


CHAPTER  V. 

FIRST  OBSERVATIONS  WITH  OPERA-GLASSES;  LUNAR  PATHS;  MOON'S  SIDE- 
REAL PERIOD;  LOCATION  OF  PLANETS;  TIME  FROM  SUN  AND  STARS; 
SIDEREAL  DAY;  SIDEREAL  AND  MEAN  SOLAR  TIME;  FURTHER  TESTS 
FOR  OPERA-GLASSES  AND  SMALL  TELESCOPE. 

55.  Sun,  moon,  and  planets  with  opera-glasses. — The  most 
brilliant  heavenly  bodies  are  not  the  ones  most  satisfactorily 
examined  with  opera-glasses.  An  average  pair,  magnifying  two 
or  three  diameters,  shows  no  disk  even  for  Jupiter  or  Venus,  and 
little  is  practicable  with  any  planet  except  to  note  the  effect  of 
the  glasses  on  color  and  brightness  (Byrd,  §  173).  For  the  sun 
ako,  observations  are  mainly  limited  to  points  like  these.  At 
first  let  an  examination  be  carefully  made  with  dark  spectacles 
only,  and  then  see  how  opera-glasses  affect  color,  size,  and 
brightness.  Note  whether  the  limb  is  ill-defined,  or  sharp  and 
clear  cut,  how  it  compares  in  brightness  with  the  center;  and 
whether  the  whole  body  appears  like  a  disk  laid  on  the  sky  or 
like  a  true  sphere.  If,  as  occasionally  happens,  there  is  a  sun 
spot  large  enough  to  be  visible,  fix  its  position  by  a  dot  marked 
on  a  circle,  representing  the  solar  disk. 

With  the  moon  rather  more  is  possible.  In  addition  to  points 
like  those  above,  see  whether  the  glasses  appear  to  have  any 
effect  upon  the  direction  and  rapidity  of  the  moon's  apparent 
motion,  what  part  of  the  field  of  view  (§  67)  is  occupied  by  the 
full  moon,  and  whether  the  terminator  appears  more  or  less 
irregular  than  with  the  naked  eye.  Different  phases  should  be 
examined,  and  sketches  made  of  the  same  phase  in  different 
lunations,  so  as  to  find  out  whether  the  markings  change  their 
position  with  regard  to  limb  or  terminator  (Byrd,  §  132).  As 
many  as  seven  of  the  "seas"  should  be  identified  with  the  help 
of  a  lunar  map. 

In  recording,  enter  the  age  of  the  moon  as  well  as  the  hour 
of  observing.  Bear  in  mind  also  that  when  opera-glasses  are 

63 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

first  used  with  any  object,  emphasis  must  be  placed  on  obtaining 
the  best  possible  focus  before  anything  else  is  attempted  (§  53). 

56.  Moon's  diurnal  path  with  and  without    instruments. — 
There  are  various  ways  to  locate  points  in  the  diurnal  path  of 
the  moon.    If  the  meridian  and  horizon  are  taken  as  reference 
lines,  only  a  few  minutes  at  the  beginning  and  end  of  the  evening 
period  are  required  for  notes  like  these:  "At  7h  P.  M.,  the  moon 
is  not  very  high  and  about  midway  between  the  meridian  and 
the  western  horizon;  At  9h  p.  M.,  it  is  near  the  distant  tree  tops 
to  the  southwest."    If  the  altitude  is  not  too  large,  a  sketch  may 
be  made  of  that  part  of  the  horizon  in  the  vicinity  of  the  moon, 
and  its  place  fixed  more  than  once  in  the  evening  by  reference  to 
trees  and  buildings,  care  being  taken  to  observe  each  time  from 
exactly  the  same  place. 

More  accurate  data  are  obtained  by  making  estimates  or 
measures.  Thus,  altitude  can  be  expressed  in  terms  of  the  alti- 
tude of  a  star  or  planet,  and  azimuth  or  amplitude  as  a  part  of 
the  quadrant  between  two  cardinal  points.  Measures  are  made 
most  conveniently  with  an  altazimuth  instrument,  as  in  finding 
the  diurnal  path  of  the  sun  (§  30).  But  the  intervals  may  well 
be  shorter,  and  the  points  fixed  fewer  in  number,  including 
usually  only  one  of  the  three  critical  points,  rising,  southing,  and 
setting.  Any  one  of  these  points  gives  the  key  to  the  moon's 
path  for  the  day  (§  80),  but  special  interest  attaches  to  places  of 
rising  and  setting.  If  for  either,  several  points  are  fixed  for 
different  phases  in  one  season,  or  for  the  same  phase  in  different 
seasons,  striking  contrasts  are  brought  out  (Byrd,  §§  139,  140). 

57.  Path  of  the  moon  among  the  stars. — When  as  many  as 
five  positions  of  the  moon  have  been  fixed  in  one  lunation  (§  46), 
they  should  be  plotted  on  the  celestial  globe.     They  ought  to 
give  data  for  determining  the  direction  and  rate  of  the  moon's 
motion,  and  its  path  through  several  constellations.     If  it  is 
practicable  to  obtain  ten  or  more  positions,  as  in  the  following 
illustration,  other  important  deductions  can  be  drawn. 

64 


MOON'S  PATH  AMONG  THE  STARS 


OBSERVATION. — During  July  and  August  1908,  I  followed  the 
course  of  the  moon  through  an  entire  lunation,  beginning  when  it 
was  three  days  old,  July  first,  and  continuing  observations  till 
after  new  moon  in  August.  Positions  were  fixed  on  15  dates, 
but  owing  to  an  unbroken  series  of  cloudy  nights,  the  latter  part 
of  July,  they  were  not  so  well  distributed  as  is  desirable.  All 


#«  Ceti, 


FIG.  9.— Moon  in  Reference  to  Stars. 

were  based  on  definite  numerical  estimates,  like  those  given 
below  for  July  21,  and  the  sketch  added  (Fig.  9)  shows  how  the 
moon  was  placed  in  reference  to  the  stars  employed  on  that  night. 
Mantoloking,  N.  J.,  3h  35m  A.  M.,  E.  s.  T.,  Tuesday,  July 
21,  1908.  The  moon  is  east  of  Aries,  and  I  estimate, 

Z ay  Ceti  0>  =90°;  7  Ceti  3)  =  If  a  7  Ceti. 
Another  estimate  gives,  7  Ceti  2)  =  1 J  a  7  Ceti. 

(J.  T.  V.) 
65 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

Not  only  as  here,  is  it  well  to  note  two  distances  in  locating  a 
heavenly  body;  but  to  make,  when  practicable,  two  completely 
independent  estimates  of  position,  and  so  lessen  the  effect  of 
accidental  errors  (Byrd,  §  3). 

To  reduce  and  discuss  a  series  of  observations  like  those  taken 
at  Mantoloking,  they  should  be  plotted  on  the  celestial  globe.  A 
number  of  details  are  involved,  and  these  are  most  readily  ex- 
plained by  describing  the  work  actually  carried  out  for  this  series. 

EXERCISE. — From  the  data  given  above,  for  the  moon  on  July 
21,  1908,  fix  its  place  on  the  globe,  and  find  its  coordinates  in 
right  ascension  and  declination. 

After  the  globe  is  adjusted  and  secured  in  position  with  the 
stars  employed  conveniently  placed,  a  rectangular  piece  of 
plotting  paper  is  used  in  locating  the  moon  (§51,  Ex.  4).  Let 
one  of  the  right  angles  be  placed  on  the  star,  y  Ceti,  one  of  its 
adjacent  sides  pass  through  a  Ceti,  and  the  other  extend  north- 
ward, as  indicated  in  Fig.  9.  The  moon's  exact  position  on  this 
side  is  fixed  by  laying  off  from  7  the  mean  of  the  two  estimated 
distances  between  it,  and  the  star. 

To  find  the  right  ascension  and  declination  of  the  point  thus 
determined,  note  that  in  its  vicinity,  51.3d,  on  the  rectangular 
paper  used,  equals  60™,  and  35. 5d  equals  10°  of  declination. 
Therefore,  as  the  place  for  the  moon  is  24.7d  east  of  the  2b- 
circle,  and  l.Od  north  of  the  10°-parallel,  north,  it  follows  that 
the  entire  right  ascension  and  decimation  are,  2h  29m  and, +  10°. 3. 
The  values  of  these  coordinates  obtained  by  interpolating  from 
the  Ephemeris  are,  2h31m,-f  10°.3  (§  50,  Ex.  2). 

In  like  manner,  all  the  fifteen  positions  are  plotted  on  the 
celestial  globe,  and  a  coarse  thread,  placed  as  symmetrically  as 
possible  in  regard  to  them  (Byrd,  §  207,  Fig.  33)  marks  out  the 
path  of  the  moon.  The  thread,  stiff  with  wax,  is  held  in  place  by 
narrow  strips  of  adhesive  paper  (§  51),  so  that  the  globe  can  be 
turned  back  and  forth  and  the  path  examined  throughout  its 
course  of  360°. 

It  is  found  to  lie  within  the  zodiacal  constellations,  except 
that  at  one  point  it  passes  over  the  boundary  line  of  Aries  into 

66 


MOON'S  SIDEREAL  PERIOD 

Cetus,  and  enters  Ophiuchus  for  a  few  degrees,  where  that  con- 
stellation extends  on  both  sides  of  the  ecliptic.  Its  farthest  dis- 
tance north  of  this  circle  is  3°.5,  farthest  south,  5°.5;  and  as 
about  half  of  it  is  above  and  half  below  the  ecliptic,  it  is  fair  to 
conclude  that  the  moon's  path  through  the  stars  is  approximately 
a  great  circle,  lying  near  the  ecliptic,  and  inclined  to  it  by  an 
angle  not  differing  much  from  5°. 

A  check  for  the  whole  path  is  obtained  by  taking  the  moon's 
right  ascension  and  declination  from  the  Ephemeris  for  the  times 
of  observation,  plotting  them  on  the  globe  and  marking  the  cor- 
responding path,  as  described  above.  Comparison  of  the  two, 
shows  that  the  path  laid  down  from  naked-eye  estimates  coin- 
cides in  places  with  that  derived  from  the  Ephemeris,  is  not  often 
1°.5  from  it  and  never  quite  2°.  It  should  be  added,  however,  that 
this  check  does  not  bring  out  clearly  errors  in  right  ascension. 

Instead  of  plotting  individual  positions,  four  critical  points 
suffice  for  an  approximate  check.  Thus,  the  intersections  of 
the  moon's  path  with  the  ecliptic,  that  is,  its  nodes  (Young, 
Art.  142)  are  located  from  the  longitude  of  the  nodes  (§  34); 
and  the  points  in  the  path  farthest  north  and  south  are  fixed, 
5°  above  and  5°  below  the  ecliptic,  just  90°  from  each  intersec- 
tion. A  small  cord,  or  fine,  flexible  wire  passed  through  the 
four  points  marks  out  the  required  path. 

58.  Moon's  rate  of  motion  and  sidereal   period. — Any  two 

positions  of  the  moon,  if  they  are  fairly  accurate  and  several 
days  apart,  give  satisfactory  data  for  determining  its  rate  of 
motion.  Take,  for  example,  the  observations  of  July  5  and  10, 
in  the  series  discussed  in  the  preceding  section.  The  arc  between 
the  corresponding  positions  plotted  on  the  celestial  globe  is  66°.0 
in  length,  and  this  divided  by  5,  the  number  of  days  intervening, 
shows  that  the  moon  was  traveling  at  the  rate  of  13°.2  a  day  or 
0°.55  an  hour.  In  like  manner,  from  the  observations  of  July  8 
and  13,  the  rates  per  day  and  hour  are  found  to  be,  12°.9  and 
0°.54.  The  mean  daily  rate  given  by  Young,  Art.  141,  is  13°  11* 
which  makes  the  hourly  rate  0°.55. 

67 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

The  sidereal  period  of  the  moon  is  the  time  it  takes  to  make 
a  complete  circuit  of  the  celestial  sphere,  that  is,  to  pass  from 
a  particular  star  back  to  the  same  star  again.  Its  length  can  be 
determined  from  the  data  of  §  57;  for  the  plotted  path  there 
described  shows  that,  on  Aug.  4,  the  moon  had  nearly  but  not 
quite  reached  the  position  occupied  July  8,  27  days  earlier. 
The  intervening  space  measures  3°. 3,  and  to  traverse  it,  the 
moon  requires  6.6  hours,  as  it  moves  practically  over  half  a 
degree  in  an  hour.  The  interval  between  the  given  dates, 
carried  to  hours,  is  26d  23h.4  and  the  6h.6  added  makes  the 
whole  sidereal  period  27d  6h. 

Another  value  for  this  period  is  obtained  in  like  manner  by 
comparing  the  observations  of  July  6,  and  Aug.  3.  On  the  latter 
date,  however,  the  moon  had  gone  beyond  the  position  of  July  6, 
a  space  equal  to  7°,  so  14  hours  is  to  be  subtracted  from  the 
interval  between  these  observations,  making  the  required  sidereal 
period  27d  9h. 

The  numerical  work  required  is,  in  brief,  as  follows : 

Time  of  Obs.,  July,     8d    9h    0*      Time  of  Obs.,  July,    6d    9h  4(T 
"      "     "   ,  Aug.,    4     8  25  "      "     "   ,  Aug.,  3     8  38 


Int.  bet.  the  two,      26  23.4  Int.  bet.  the  two,    27  23 

T.  for  0)  to  go  3°.3,          6.6  T.  for  0)  to  go  7°,         14 


Sidereal  Period,        27     6  27     9 

Young,  Art.  141,  gives  27d  7h.7  as  the  average  period. 

59.  Planets  mapped  in  reference  to  stars. — The  study  of 
planetary  motion  is  based  upon  fixing  at  a  definite  time  an 
accurate  position  of  a  planet  among  the  stars.  This  is  effected 
just  as  in  mapping  the  moon,  except  that  stars  can  be  employed 
which  are  fainter  and  nearer  the  body  observed. 

The  following  examples  illustrate  the  location  of  single  points, 
and  it  is  only  necessary  to  obtain  a  number  in  order  to  trace 
the  path  of  a  planet  through  the  constellations  (§83). 

68 


PLANET  IN  REFERENCE  TO  STARS 


OBSERVATION  1. — W.  V.  Lawrence,  Kan.,  Tuesday,  Sept.  3, 
1907.  Between  eight  and  nine  this  evening,  Mars  occupies  an 
unusually  favorable  position;  for  it  is  almost  exactly  at  the 
intersection  of  two  star-lines,  o  £  and  r  0,  i.  e.,  the  diagonals  of 
the  bowl  of  the  "milk  dipper"  in  Sagittarius. 

OBSERVATION  2. — 84  Elm  Street,  Northampton,  Mass.,  8h 
p.  M.,  E.  s.  T.,  Monday,  March  16,  1908.  It  is  the  night  before 
full  moon,  and  faint  stars  cannot  be  seen  in  mapping  Jupiter. 
As  usual  I  make  a  rough  sketch  showing  how  the  planet  is 
placed  among  the  stars,  as  well  as  the  following  numerical  esti- 
mates of  distance  and  angle: 

Position  L—  Z  ft  Gem.  Qi  a  Can.  Min.  =  90° 

ft  Gem.  01  =|  a  Can.  Min.  Qt  =3  a  ft  Gem. 

Position  II.— Z  y  a  Gem.  Qj.  =90°;  a  Gem.  Qt  =  J  a  y  Gem. 

(A.  E.  T.) 

To  find  where  these  planets  were  situated  on  the  celestial 
sphere  at  the  times  of  observation,  there  is  no  better  method 
than  plotting  on  the  celestial  globe,  as  in  §  57.  When,  as  above 
for  Jupiter,  two  places  are  fixed,  the  final  observed  position  is  to  be 
taken  just  midway  between  the  two  points  plotted,  though  if  pre- 
ferred, the  coordinates  of  each  point  may  be  read  and  the  mean 
taken.  Corrections  for  precession  require  little  extra  labor  (Byrd, 
§  57),  and  are  properly  included,  as  in  the  following  table,  which 
contains  the  final  right  ascensions  and  declinations  of  both  planets. 

TABLE  IV.— POSITION  OP  cf ,  SEPT.  3,  '07.    POSITION  OP  01,  MAR.  16,  '08. 


R.  A., 
Corr.  for  Free., 

Corrected  R.  A., 
Decl., 
Corr.  for  Free., 

Corrected  Decl., 

FR.  OBS.  AND 
GLOBE. 

FR.  EPHEM. 

FR.  OBS.  AND 
GLOBE. 

FR.  EPHEM. 

18h    48m 
+  2 

18h    51m 
-27°.  5 

gh      16m 

+2 

8h    26m 
+20°.  1 

18    60 
-27°.  9 
+   0.1 

8    18 
+20°.  9 
-  0  .1 

-27  .8 

+20  .8 

69 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

To  facilitate  comparison,  the  coordinates  from  the  Ephemeris 
are  inserted  opposite  the  corrected  values,  derived  from  ob- 
servation. 

60.  Conjunction  of  planets. — When  one  bright  planet  passes 
another,  the  points  to  be  noted  are,  their  relative  positions,  and 
the  distance  between  them  at  the  time  of  conjunction,  though 
this  is  not  necessarily  the  smallest  distance;  for  conjunction 
signifies  merely  that  heavenly  bodies  have  the  same  longitude 
or  right  ascension.  The  time  to  observe  is  on  the  date  of  con- 
junction given  in  the  small  almanacs,  and,  if  clouds  permit,  it 
is  well  to  include  also  the  night  before  and  the  one  following. 

OBSERVATION. — Ridgmont,  Greenfield,  Mass.,  8hp.  M.,  E.S.  T., 
Friday,  April  3,  1908.  In  the  west,  not  far  above  the  horizon, 
Venus  and  Mars  are  seen  near  together,  Venus  being  a  little 
higher  and  to  the  east  of  Mars.  I  estimate  that  the  distance 
between  them  is  just  equal  to  that  separating  two  of  the  stars 
in  the  belt  of  Orion,  that  is, 

Distance  bet.  9  and  cT  =6  €  Orionis. 

The  following  evening,  April  4,  is  the  almanac  date  of  con- 
junction, and  from  the  same  place  at  8h  p.  M.,  I  look  again  afc 
the  planets.  There  is  only  a  slight  change  in  position,  I  estimate, 

Dist.  bet.  9  and  cf  =  |  5  e  Orionis. 

Owing  to  clouds,  no  observation  could  be  taken  on  the  third 
night.  (B.  F.  F.) 

The  distance  measured  on  the  globe  between  the  plotted  posi- 
tions of  5  and  €  Orionis  is  1°.4  (§  51,  Ex.  3),  and  calculation 
gives  the  same  value  (Byrd,  §  72).  Therefore,  according  to 
observation,  these  planets  were  separated  by  1°.4  at  8h  p.  M., 
April  3,  and  at  the  same  hour,  April  4,  by  1°.6,  giving  a  mean 
distance  of  1°.5  at  the  mean  of  the  astronomical  times  of  ob- 
serving, April  3d  20h  (§35).  Reference  to  the  Ephemeris  whichr 
of  course,  was  not  consulted  beforehand  by  the  observer,  shows 
that  the  actual  time  of  conjunction  was  April  3d  22h,  and  that 
Venus  was  then  1°  37'  north  of  Mars. 

70 


TIME  FROM  A  WINDOW  GNOMON 

61.  Time  and  meridian  line  from  the  gnomon. — If  the  common 
form  of  gnomon  is  employed,  it  must  be  carefully  adjusted, 
especially  is  it  essential  that  the  east  edge  of  the  upright  should 
be  vertical  to  the  meridian  line  (Byrd,  §  112,  Obs.  3).  To  bring 
the  shadow  out  sharply,  paste  strips  of  white  paper  over  a  large 
part  of  the  line,  leaving,  however,  a  small  section  near  each  end, 
so  that  with  a  ruler  the  whole  line  can  be  drawn  on  the  paper. 

Preparations  should  be  completed  a  few  minutes  before  sun 
noon,  in  order  that  the  observer  may  give  undivided  attention 
to  the  moving  shadow.  When  it  coincides  with  the  meridian  line, 
the  word  "time"  or  better,  "tip"  is  called,  and  the  recorder  notes 
the  second,  minute,  and  hour.  If  the  time-piece  is  set  to  standard 
time,  its  error  is  found  as  described  a  little  later  in  this  section. 

The  converse  of  this  observation  lies  in  marking  a  north  and 
south  line,  when  the  time  of  sun  noon  is  known.  Let  the  line 
already  drawn  be  entirely  covered  with  paper  to  prevent  any 
bias  in  its  favor,  and  the  observer  be  in  readiness  a  little  before 
noon.  At  the  signal  for  this  instant,  two  marks  should  be  made 
quickly,  the  first  at  the  edge  of  the  shadow  well  to  the  north, 
and  the  second  near  the  gnomon.  In  both  exercises  the  edge  of 
the  shadow  is  to  be  taken  about  midway  between  the  umbra 
and  the  penumbra  (§  43). 

The  following  determination  of  watch  error  illustrates  the  use 
of  the  solar-image  gnomon: 

OBSERVATION.— N.  C.,New  York,  N.  Y.,  Monday,  June  9, 1913. 
To  find  time,  I  employ  the  gnomon  described  in  §  31,  taking 
note  of  the  sun's  image  formed  by  the  single  aperture  over  me- 
ridian line  No.  I,  reckoned  from  the  east.  As  this  image  ap- 
proaches the  meridian,  I  watch  it  closely  and  call  "tip"  when 
it  seems  bisected.  A  little  later  as  the  image  still  appears  to 
be  bisected,  I  call  "tip"  a  second  time.  The  record  obtained  is, 

llh  55m  44s  1  Rec.  B.  G. 

49  /  Watch,  Ingersoll  No.  2.        (E.  B.). 

Since  the  watch  employed  was  set  to  eastern  standard  time, 
the  reduction  of  the  observation  consists  in  finding,  from  this 

71 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

standard  time  of  apparent  noon,  how  many  seconds  the  watch 
was  fast  or  slow.  If  the  rigorously  correct  time  of  apparent 
noon  were  known,  the  difference  between  that  and  the  observed 
time  would  give  at  once  the  error  sought.  But  this  "rigorously 
correct  time"  is  simply  apparent  time  converted  to  standard 
time,  an  operation  which  requires  only  two  steps,  the  change  of 
apparent  noon  to  the  corresponding  local  mean  time,  and  that 
in  turn  to  standard  time  (§  38,  Ex.  5). 

In  concise  form  the  reduction  is  as  follows: 

Sun  noon,  apparent  time,  12h  (XT  OO1 

Equation  of  time,  —  1      3 


Local  mean  time  of  sun  noon,  11    58    57 

Stand.  Merid.  west  of  New  York,  4     9 


Stand,  time  of  sun  noon  fr.  calculation,          11   54   48 
Stand,  time  of  sun  noon  fr.  observation,         11    55    46 


Watch  fast  by  this  observation,  58 

The  true  error  of  the  watch  was  obtained  by  comparing  it  by 
telephone  with  the  standard  clock  of  the  Western  Union  Time 
Service,  and  was  found  to  be  lm  10"  fast,  making  the  error  of 
observation  12s. 

62.  Time  from  meridian  transit  of  sun  or  stars. — The  fall  and 
winter  when  the  sun  runs  low  are  favorable  seasons  for  deter- 
mining time  from  the  sun's  noon  transit  over  plumb  lines. 
These  may  be  supported  and  adjusted  in  different  ways,  but  it 
is  desirable  to  have  them  under  shelter. 

OBSERVATION  1. — W.  V.,  Lawrence,  Kan.,  Saturday,  Nov.  25, 
1911.  The  plumb-line  booth,  used  in  observing  the  sun's  transit 
today,  is  like  that  described  in  §  9.  The  two  plumb  lines, 
which  fix  the  meridian,  owing  to  the  sun's  low  declination,  are 
satisfactorily  placed  three  feet  apart,  the  one  at  the  north  being 
hardly  a  third  as  thick  as  that  near  the  south  opening. 

72 


TIME  FROM  SUN  AND  STARS 

Nine  times  are  noted,  that  is,  the  transit  of  west  limb,  center, 
and  east  limb  over  each  of  three  pair  of  lines.  These  are  desig- 
nated in  the  record  as  west,  central,  and  east  pair. 

STANDARD  TIMES  OF  SUN'S  TRANSIT. 

West  Pair— West  limb,         12h    Im208 
Center,  2   40 

East  limb,  4     0 


Mean,  2  40 

Central  Pair— West  limb,  6  8 

Center,  7  44 

East  limb,  9  20 


Mean,  7  44 

East  Pair— West  limb,  10  58 

Center,  12  40 

East  limb,  14  8 


Mean,  12   35 

Final  mean,  12     7   40 

Since  the  true  time  of  transit,  found  as  in  the  preceding  section, 
is  12h  8m  5fl,  the  combined  error  of  watch  and  observation  is, 
+25";  but  comparison  with  jeweler's  time,  makes  the  watch 
slow  17",  and  so  according  to  this  test,  the  error  of  observation 
is  8'. 

A  week  later,  another  observation  of  the  sun,  made  and  tested 
in  like  manner  was  found  to  be  in  error  2s  (Obs.  2). 

Astronomers  invariably  obtain  accurate  time,  not  from  the 
sun,  but  from  the  stars,  that  is,  they  find  directly  the  error  of 
a  sidereal  clock  or  chronometer.  Beginners  also  may  employ  a 
similar  method,  for  any  watch  serves  as  a  sidereal  time-piece,  if 
two  changes  are  made.  It  should  be  regulated  to  gain  about 
four  minutes  a  day  on  mean  time,  and  the  hands  set  forward  or 

73 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

backward  to  mark  sidereal  time  (§  64,  Ex.).  Indeed,  the  latter 
correction  alone  suffices,  when  the  period  of  observation  is  short. 

OBSERVATION  2. — W.  V.,  Lawrence,  Kan.,  Saturday,  March  16, 
1912.  The  transit  of  Sirius  is  taken  from  the  plumb-line  booth 
used  in  observation  1,  but  the  upper  part  of  the  south  aperture  is 
left  entirely  open,  and  the  lines,  the  same  as  for  the  sun  at  this 
season,  are  separated  by  two  feet.  They  are  all  satisfactorily 
lighted  by  a  single,  small,  kerosene  lantern;  and,  when  adjust- 
ments are  made,  the  one  at  the  south  shows  as  a  narrow  white 
band,  and  those  at  the  north,  when  properly  projected,  as  black 
lines  through  its  center. 

The  following  record  is  made  from  an  Elgin  watch,  set  to 
sidereal  time,  where  for  each  pair  of  lines  two  times  are  noted 
(Obs.  1),  the  first,  as  soon  as  the  star  seems  bisected,  and  the 
second  when,  if  anything,  that  instant  is  passed. 

SIDEREAL  TIMES  OF  THE  TRANSIT  OF  SIRIUS. 

West  Pair,  6h  33m  45" 

34   12 


Mean,  33   58 

Central  Pair,  40   38 

41     8 


Mean,  40   53 

East  Pair,  47    10 

40 


Mean,  47  25 

Final  mean,  obs.  time  of  transit,  6  40  45 

Ephem.  R.  A.,  sid.  T.  of  transit,  6  41  16 

Watch  slow  by  observation,  31 

According  to  jeweler's  time,  the  correct  error  of  the  watch  was, 
+32,  making  the  error  of  observation  1s,  too  small  an  error,  how- 
ever, to  be  considered  trustworthy  in  naked-eye  observing. 

74 


•      LENGTH  OF  SIDEREAL  DAY 

63.  Sidereal  day  from  star  transits. — A  sidereal  day  is  the 
interval  between  two  successive  transits  of  the  same  star  across 
the  meridian.  Its  length  is  usually  given  by  comparing  it  with 
the  mean  solar  day,  which  is  the  interval  between  two  sucessive 
transits  of  the  sun  over  the  meridian.  The  latter  may  also  be 
defined  as  any  period  of  24  hours,  marked  off  by  a  clock  or 
watch  keeping  mean  time,  provided  there  is,  meanwhile,  neither 
gain  nor  loss. 

The  comparison  between  the  two  days  is  effected  by  observing 
the  transit  of  a  star  on  one  night,  and  the  transit  of  the  same 
star  over  the  same  reference  line  on  the  following  night,  a  mean- 
time watch  being  used  in  recording.  Assume  for  a  moment  that 
the  observations  are  perfect,  and  that  the  watch  keeps  perfect 
time,  then  the  three  possible  relations  between  the  days  are 
stated  thus: 

If  the  second  transit  of  the  star  comes  at  the  same  time  as 
the  first,  the  days  are  equal;  if  later,  the  sidereal  day  is  the 
longer;  if  earlier,  the  sidereal  day  is  shorter  than  the  mean 
solar  day.  In  dealing  with  actual  observations,  watch  errors 
must  be  taken  into  account,  and  it  is  desirable  to  have  an  in- 
terval of  a  week  or  more  between  the  transits  so  as  to  reduce 
the  effect  of  errors  in  observing. 

OBSERVATION. — S.  C.  O.,  Northampton,  Mass.,  Oct.,  1905. 
During  this  month  the  transit  of  the  star  Fomalhaut  was  ob- 
served twice  over  the  same  plumb  lines  which  remained  fixed  in 
position  (§8).  The  times  of  transit,  taken  from  a  mean-time 
watch,  were,  8h  39m  40s  and  8h  12m  108,  the  watch  being  slow 
41s  on  the  first  night  and  29s  on  the  second.  The  observed 
times,  therefore,  corrected  for  watch  errors  make, 

Fomalhaut's  time  of  transit,  Oct.  9,  8h  40m  21s 

"     "         "         "      16,  8  12   39 

Second  time  of  transit  earlier  than  first,  27   42 

(S.  S.) 

Since,  after  an  interval  of  7  days,  the  star  crossed  the  reference 
line  nearly  28  minutes  earlier  than  at  first,  after  one  day's  in- 

75 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

terval,  it  would  cross  about  4  minutes  earlier.  The  calculation 
carried  to  seconds  makes  the  sidereal  day  shorter  than  the 
mean  solar  by  3m  57",  a  second  larger  than  the  true  value, 
3m  55".9  (Comstock's  Field  Ast.  19  (19)).  In  exercises  like  this, 
where  the  difference  between  observations  is  taken,  an  error  of 
one  second  is  a  more  satisfactory  test  of  accuracy  than  for  a 
single  determination  of  time  (§  62,  Obs.  2). 

A  moment's  consideration  shows  that  this  gain  of  sidereal 
time  is,  in  reality,  a  measure  of  the  sun's  apparent  motion. 
Thus,  assume  that  the  sun  and  reference  star  cross  the  plumb 
lines  at  the  same  instant  on  a  given  day,  on  that  following,  the 
sun  will  cross  nearly  four  minutes  later  than  the  star;  and,  as 
the  star  is  practically  a  fixed  point,  the  difference  in  the  time  of 
transit,  3m  57s,  according  to  this  observation,  is  the  daily  rate 
at  which  the  sun  appears  to  move  eastward  among  the  stars. 

Furthermore,  if  it  be  taken  as  a  known  fact  that  this  motion 
of  the  sun  is  nearly  uniform  in  a  great  circle  of  the  sphere,  the 
length  of  the  year  may  be  ascertained  approximately.  For  360° 
or  24  sidereal  hours,  divided  by  the  sidereal  gain  in  one  day, 
gives  the  number  of  days  required  for  the  sun  to  pass  from  a 
given  position  in  regard  to  the  stars  back  to  the  same  position 
again;  and  this  is  by  definition  a  year  (Young,  Art. 133).  The 
daily  gain  found  above  by  observing  Fomalhaut  is  in  mean 
time,  reduced  to  sidereal  by  Table  III  of  the  Ephemeris,  it 
becomes  3m  578.6  (i.  e.,  0°.99,  see  §  41,  Obs.),  and  24h  divided  by 
this  interval  makes  the  length  of  the  year  363.6  days. 

A  more  trustworthy,  and  probably  more  accurate  result, 
would  be  obtained  by  taking  the  mean  of  a  large  number  of 
observations,  though  here  the  watch  errors  have  been  deter- 
mined more  accurately  perhaps  than  in  many  instances. 

64.  Relation  between  sidereal  and  mean  solar  time. — Accord- 
ing to  the  preceding  section,  sidereal  time  gains  3m  57"  (3m.95) 
a  day  on  mean  solar  time  or  about  10"  an  hour.  This  rate  is 
usually  accurate  enough  for  reducing  hours  and  minutes  in 
either  time  to  the  corresponding  interval  in  the  other;  but,  if 

76 


TIMES  OF  MOON'S  PHASES 

desired,  exact  corrections  can  be  taken  from  the  Ephemeris, 
Tables  II  and  III.  When,  instead  of  dealing  with  intervals  of 
time,  it  is  required  to  convert  the  time  of  day  from  mean  solar 
to  sidereal  time,  or  vice  versa,  the  operations  involved  are  more 
complicated  (Byrd,  §§  51-53).  It  is  not  difficult,  however,  to 
make  an  approximate  reduction,  since  sun  and  star  time  agree  at 
the  vernal  equinox  and  at  the  autumnal,  differ  by  12  hours. 

EXAMPLE. — After  Nov.  6,  1909,  the  right  ascension  of  Polaris 
to  the  nearest  minute  is  lh  27m  for  the  remainder  of  the  month 
(Ephemeris,  p.  322).  What,  approximately,  is  its  mean  time  of 
meridian  transit,  Nov.  12,  1909? 

Since  a  star's  right  ascension  is  its  sidereal  time  of  meridian 
passage  (§  49),  the  requirement  is  really  to  reduce  a  given  side- 
real to  mean  solar  time.  Two  corrections  must  be  applied,  one, 
the  difference  at  the  autumnal  equinox,  between  sidereal  and 
mean  solar  time;  the  other,  the  gain  of  sidereal  on  mean  solar 
time  during  the  interval  of  50  days  between  the  equinox  and 
the  given  date,  Nov.  12.  The  whole  of  the  former  correction 
is  12h  8m  (Jayne's  Almanac,  p.  19),  and  the  latter  is  3m.95  x  50, 
or  3h  17m.5.  The  two  combined  equal  15h  26m,  which  sub- 
tracted from  the  sidereal  time,  lh  27m,  gives  10h  lm.  By  the 
rigorous  solution  10h  Om  is  obtained  (§  38,  Ex.  4),  and  in  Jayne's 
Almanac  this  is  the  time  given. 

65.  Times,  at  different  meridians,  for  the  moon's  phases. — 

The  instant  of  any  phase  of  the  moon  depends  upon  the  relative 
positions  of  sun,  earth,  and  moon,  and  is  in  nowise  affected  by 
the  location  of  the  observer.  One  determination  of  time,  there- 
fore, suffices  and  if  that  is  made  for  Greenwich,  the  time  of  any 
other  place  is  found  by  reducing  Greenwich  time  to  that  of  the 
given  meridian  (§  48). 

EXAMPLE. — Required  to  find  what  day,  hour,  and  minute 
should  be  given  in  Jayne's  Almanac  for  first  quarter  of  the 
moon  in  Oct.  1908. 

Since  this  almanac  is  calculated  for  the  meridian  5  hours  west 
of  Greenwich,  that  is  the  interval  to  subtract  from  the  Green- 

77 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

wich  time  of  the  phase,  2d  18h  14m  (Ephemeris,  p.  175),  to  ob- 
tain the  almanac  time,  which  is  2d  13h  14m,  or  in  civil  reckon- 
ing, Oct.  3d  lh  14m  A.  M.  (§  35),  and  this  is  the  time  given  in 
Jayne's  Almanac,  p.  21. 

Washington  instead  of  Greenwich  times  may  be  taken  from 
the  Ephemeris,  but  more  changes  of  sign  are  involved,  if  all 
sections  of  the  country  are  considered. 

66.  Times  of  the  phases  of  a  lunar  eclipse. — Any  phase  of  a 
lunar  eclipse,  like  the  phase  of  the  moon,  occurs  at  one  and  the 
same  absolute  instant  of  time  wherever   observed.    It  follows, 
then,  that  Greenwich  time  being  given,  any  local  or  standard 
time  required  is  obtained  as  in  §  65  by  reducing  Greenwich  time 
to  that  of  the  given  meridian. 

EXAMPLE. — The  Greenwich  time  for  the  middle  of  the  partial 
lunar  eclipse,  July  24,  1907,  was  16h  22m,  what  was  the  corre- 
sponding local  time  at  Santa  Fe,  N.  M.  ? 

The  longitude  of  the  place  is  7h  4m  W.  (Appendix),  and  this 
time  subtracted  from  the  Greenwich  time  above  gives  &  18m 
p.  M.,  as  the  required  local  time  at  Santa  F6  (Jayne's  Almanac, 
1907,  p.  1). 

67.  Field  of  view  and  magnifying  power  of  opera-glasses. — 
The  circle  of  light  seen  when  opera-glasses  are  pointed  at  the 
sky  ( §  52)  shows  how  much  space  is  visible  at  one  time,  and  that 
is  the  field  of  view  of  the  glasses.    There  is  no  object  in  deter- 
mining it  rigorously,  but  its  value  is  easily  found  approximately 
either  from  moon  or  stars.     Thus,  with  the  full  moon  in  the 
field  of  view,  estimate  how  many  moons,  placed  close  together, 
would  be  required  to  reach  centrally  across  the  field,  and  half 
that  number  is  the  diameter  of  the  field  in  degrees  (Young,  Art. 
152).    If  stars  are  employed,  pick  out  two  near  the  equator,  and 
just  far  enough  apart  so  that  both  can  barely  be  brought  into 
the  field  together,  i.  e.,  appearing  practically  at  the  extremities 
of  one  of  its  diameters.    The  distance  between  them,  measured 
on  map  or  globe,  gives  approximately  the  diameter  sought. 

78 


POWER  OF  OPERA-GLASSES 

To  find  the  magnifying  power  of  opera-glasses,  it  is  necessary 
to  ascertain  how  they  affect  the  diameter  of  an  object.  If,  for 
example,  the  magnified  image  has  a  diameter  three  times  as 
great  as  that  of  the  object  itself,  the  power  of  the  glasses  is  said 
to  be  three.  In  making  this  test,  it  is  at  first  often  difficult  to  get 
at  the  same  time  a  clear,  steady  view  of  the  object  and  its  mag- 
nified image;  and  to  place  and  hold  the  latter  while  estimates 
are  being  made.  It  is  not  amiss,  therefore,  to  give  a  preliminary 
exercise  to  practice,  and  defer  till  later  the  record  of  estimates. 
Details  are  best  illustrated  by  an  example. 

EXERCISE. — Fraser  Hall,  State  University,  Lawrence,  Kan., 
llh  A.  M.,  Saturday,  March  13,  1909,  I  take  first  a  piece  of 
plotting  paper  on  which  some  of  the  lines  have  been  reinforced 
with  black  ink,  so  as  to  mark  out  very  distinctly  three  rect- 
angles. This  paper,  fastened  to  stiff  cardboard,  is  fixed  in  a 
vertical  position  some  distance  from  where  I  sit.  Turning  the 
opera-glasses  toward  it  and  using  both  eyes,  I  focus  carefully 
on  an  irregular  cross  drawn  on  the  paper.  Then,  looking  directly 
at  the  rectangles  with  the  right  eye,  and  with  the  other  through 
the  glasses,  I  bring  the  magnified  image  of  the  one  on  the  left 
to  coincide  exactly  with  the  left-hand  side  of  the  figure  itself. 
In  thia  position,  the  magnified  image  appears  to  extend  over 
2.4  diameters  of  the  unmagnified  rectangles. 

To  obtain  another  test,  I  focus  the  glasses  on  a  window 
with  three  panes  in  the  width  of  the  sash,  and  find  that  the 
image  of  the  pane  on  the  left  covers  2.5  panes  as  seen  directly. 

(J.  F.  B.) 

Whatever  object  is  employed,  the  eye  should  be  as  far  from  it 
as  possible,  so  that  the  focus  will  differ  but  little  from  that 
used  with  heavenly  bodies.  The  mean  of  five  or  six  measures 
made  on  two  dates  gives  a  satisfactory  value  for  the  magnifying 
power,  a  power  that  should  always  be  expressed,  as  here,  in 
diameters,  not  in  areas. 

68.  Focal  length  and  field  of  view  of  small  telescope. — To 
find  the  focal  length  of  a  small  telescope,  remove  the  eye-piece, 

79 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

direct  the  tube  toward  the  sun,  and  let  its  image  fall  on  a  piece 
of  white  cardboard  held  near  the  eye  end.  Keeping  the  card  at 
right  angles  to  the  axis  of  the  tube,  shift  it  back  and  forth  till 
the  sharpest  image  of  the  sun  is  obtained,  and  then  measure 
the  distance  between  the  card  and  the  end  of  the  tube.  This 
distance  added  to  the  length  of  the  main  tube  gives  the  focal 
length,  approximately  (Byrd,  §  20,  6). 

The  field  of  view  differs  with  different  eye-pieces.  Its  diameter, 
expressed  in  time,  is  the  interval  required  for  a  star  on  the 
equator  to  pass  centrally  across  the  field.  In  making  the  actual 
determination,  however,  a  star  that  has  high,  north  declination 
is  to  be  preferred,  though  it  is  desirable  to  observe  more  than  one. 

OBSERVATION. — Williston  Observatory,  Mt.  Holyoke  College, 
South  Hadley,  Mass.,  Tuesday,  June  2,  1908.  In  order  to  find 
the  field  of  view  of  a  portable  telescope,  aperture  2.5  inches, 
and  eye-piece  magnifying  24  diameters,  I  observe  a  Virginis. 
The  telescope  is  directed  to  the  star  a  little  before  it  reaches  the 
meridian,  and  the  following  times  recorded  from  a  common  watch: 

a  Virginis  enters  field,    8h  18m  31s 
a       "       leaves      "       8  24     18 

The  watch  interval  for  the  passage  of  this  star  is  then  5m  478 
or  5m  48s,  in  sidereal  time,  and  the  reduction  to  the  equator, 
is  made  as  follows,  by  multiplying  by  the  cosine  of  the  star's 
declination : 

log  5m  48"  =  log  348",  2.5416 

log  cos  Decl.  =  log  cos  (- 10°.7),    9 . 9924 


log  of  equatorial  interval,  2 . 5340 

equatorial  interval,  5m  42s 

This  value  combined  with  another  obtained  from  the  same 
star,  and  with  one  from  a  Cephei,  gives  a  mean  result  of  5m 
39*  or  1°  25'.  That  is,  with  this  telescope  and  eye-piece,  the 
section  of  the  heavens  visible  at  one  time  is  a  circle  with  a  diam- 
eter of  1°.4,  measured  on  the  equator.  (A.  L.  O.) 

80 


CHAPTER  VI. 

FIRST  OBSERVATIONS  WITH  TELESCOPE;  LUNAR  ECLIPSES; COMETS; APPEARANCE 
AND  MOTION  OF  STARS;  POSITION  OF  EQUATOR,  ECLIPTIC,  AND  MILKY 
WAY;  LATITUDE  FROM  STARS;  TIME  FROM  SUN-DIAL;  CHARTING  DIURNAL 
PATHS;  MAGNIFYING  POWER  OF  TELESCOPE;  PROFICIENCY  OF  OBJECT- 
GLASS. 

69.  Sun  and  moon  with  small  telescope. — The  allotment  of 
time  in  due  proportion  among  different  kinds  of  observations 
will  not  leave  many  hours  for  the  telescope,  and  several  must  be 
devoted  to  preliminary  tests  and  adjustments  (§  §  53,  54,  68,  81). 
An  ambitious  program  should  not  be  undertaken  with  any  heav- 
enly body.  For  the  sun,  three  or  four  periods,  about  fifteen 
minutes  in  length,  ought  to  suffice  for  reviewing  points  suggested 
with  opera-glasses  (§  55),  and  for  examining  sun  spots  on  different 
days,  to  find  in  what  direction  they  are  moving,  and  what  changes 
take  place  in  a  short  interval.  Even  with  a  small  telescope  the 
solar  disk  may  be  studied  from  projections  on  white  cardboard, 
but  direct  views  are  more  satisfactory;  and  if  the  objective  is 
less  than  three  inches,  the  eyes  can  be  protected  by  placing  several 
pieces  of  colored  glass  in  a  cap  covering  the  eye-piece.  It  is 
hardly  safe,  however,  to  trust  to  one  piece  of  glass,  no  matter 
how  thick  and  dark. 

Rather  more  time  should  be  given  to  the  moon  than  to  the  sun; 
for,  with  a  small  telescope,  more  can  be  seen  on  the  moon  than 
on  any  other  heavenly  body.  Two  observing  periods,  an  hour 
in  length,  serve  very  well,  provided  they  come  in  different  luna- 
tions. In  the  first,  progress  will  doubtless  be  slow,  if,  as  often 
happens,  use  is  first  made  of  the  telescope  in  studying  the  moon; 
but  at  the  end  of  the  second,  there  should  be,  in  all,  as  many  as 
twenty  objects  identified.  More  than  twice  that  number  can  be 
sketched  in  an  hour  by  an  experienced  observer  when  the  phase 
of  the  moon  is  favorable  (Byrd,  §  216). 

81 

6 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

Whenever  a  telescope  is  used  in  observing,  it  is  essential  to 
state  in  the  notes  the  aperture  of  the  objective  and  the  magni- 
fying power  employed. 

70.  Lunar  eclipses. — Eclipses  of  the  moon  afford    excellent 
training  for  beginners  in  seeing  and  recording.     Unlike   many 
observations,  they  present  a  continuous  series  of  phenomena, 
extending  over  a  considerable  length  of  time,  and  marked  by  a 
beginning,  culmination,  and  decline.     In  preparing  to   observe 
them,  a  list  of  exercises  should  be  made  out  and  studied  before- 
hand (§  82,  Byrd,  §§  133,  149),  so  that  during  the  eclipse  no  time 
need  be  lost  in  planning  what  to  do  and  when  and  how  to  do  it. 
Most  of  the  observations  should  be  made  with  the  unaided  eye, 
but  if  there  has  been  some  practice  with  opera-glasses  and  small 
telescope,  they  are  properly  used  in  connection  with  a    few 
points. 

Lunar  eclipses  are  not  an  every-day  occurrence,  and  when  one 
does  come  during  the  astronomical  course,  it  merits  a  generous 
amount  of  time  and  attention. 

71.  Shooting   stars. — Notwithstanding  the  rapid    motion  of 
shooting  stars,  practice  enables  the  observer  to  decide  definitely 
about  a  number  of  their  characteristics ;  as,  for  example,  how 
they  are  moving  with  regard  to  the  horizon,  how  they  compare 
in  color  and  brightness  with  stars  or  planets,  whether  they  are 
followed  by  trains  of  light,  whether  there  are  differences  in  their 
rates  of  motion,  and  where  they  appear  and  disappear,  that  is, 
in  what  part  of  a  particular  constellation  they  are  seen  at  first 
and  at  the  last. 

On  almost  every  evening,  when  it  is  clear,  some  shooting  stars 
are  seen,  and  on  certain  dates  their  number  is  large,  and  their 
fall  is  known  as  a  meteoric  shower.  That  of  the  Leonids  is  one 
of  the  most  noted  (Byrd,  §  178). 

72.  Appearance  and  motion  of  bright  comets. — Once  in  about 
three  or  four  years,  on  the  average,  a  comet  appears  that  is  vis- 

82 


APPEARANCE  OF  BRIGHT  COMETS 

ible  to  the  naked  eye,  and  at  longer  and  more  irregular  intervals, 
a  really  bright  one  is  seen,  like  that  discovered  by  Zaccheus  Daniel 
in  June,  1907. 

Beginners,  as  well  as  astronomers,  should  be  interested  both 
in  the  motion  of  comets  on  the  celestial  sphere,  and  in  their 
physical  appearance.  Thus,  a  complete  record  should  include 
estimates  of  distance  and  angle  for  locating  the  head  or  nucleus, 
among  the  stars;  and  careful  notes  regarding  color  and  brightness  r, 
and  the  size  and  form  of  the  constituent  parts.  Since  the  interest 
and  value  of  observations  increase  with  their  number,  a  comet 
should  be  followed  as  long  as  it  is  visible  with  opera-glasses,  and 
some  data  obtained,  if  possible,  on  every  clear  night. 

In  partial  illustration  of  these  suggestions,  the  following  ex- 
amples are  given: 

OBSERVATIONS  1. — W.  V.,  Lawrence,  Kan.,  Monday,  Aug.  26,. 
1907.  The  moon,  which  is  now  midway  between  full  and  last 
quarter,  lights  up  the  eastern  sky,  there  are  also  some  clouds,  and 
twilight  is  approaching;  but  in  spite  of  these  drawbacks,  Daniel's 
comet  is  fairly  bright  at  4h,  A.  M.,  c.  s.  T.,  and  remains  visible 
to  the  naked  eye  till  nearly  5  o'clock.  Opera-glasses  show  little 
detail,  but  a  small  telescope,  with  an  eye-piece  magnifying  60 
diameters  (§  81),  gives  a  good  view  of  the  head.  It  is  large  and 
bright,  the  light  seeming  to  be  in  streams,  as  if  from  a  flowing 
fountain.  The  nucleus  has  a  tinge  of  yellow,  is  oval  in  shape  and 
eccentrically  placed.  The  whole  effect  resembles  that  depicted 
for  the  great  comet  of  1882,  except  that  the  outer  envelope 
spreads  farther  away  from  the  axis,  leaving  larger  dark  rifts  on. 
either  side.  ("Young's  General  Astronomy,"  Art.  751.) 

A  few  days  later,  the  head  was  found  to  be  much  smaller  and 
the  fountain-like  effect  had  disappeared. 

OBSERVATION  2. — 519  Oakland  Avenue,  Pasadena,  Calif.,  Sat- 
urday, Sept.  7,  1907.  Looking  out  about  4h,  A.  M.,  p.  s.  T., 
I  find  Daniel's  comet  appearing  just  above  the  horizon.  The 
seeing  is  excellent,  and  I  can  follow  the  tail  with  the  unaided  eye 
nearly  20°.  It  extends  upward  and  a  little  to  the  south,  that  is, , 
it  points  away  from  the  sun. 

83 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

In  order  to  fix  the  comet's  position,  I  employ  three  comparison 
stars,  a  and  0  Cancri  and  f  Hydrse,  as  shown  in  Fig.  10.  The 
comet's  distance  from  a,  I  estimate  as  three  fourths  that  be- 
tween a.  and  /?  and  also  one  and  a  half  times  that  between 
a  and  f .  The  line  connecting  /3,  a,  and  the  comet  is  not  quite  a 
straight  line  but  bends  downward  a  little  at  /3,  and  the  angle  at 
a  between  £  and  the  comet  is  a  little  more  than  a  right  angle. 
My  final  numerical  estimates  are,  therefore: 

Position  1. —  Z  /3  a  Cancri  <&.  =  175°,  a  Cancri  &  =  f  a  0  Cancri. 
Position  2. —  Z  £  Hydrae  a  Cancri  <&.  =  95°,  a  Cancri  <&  — l\  a  Can- 
cri f  Hydrse. 


•f  fl  Guicr? 


+a  Cdncri 

*£ 


FIG.  10. — Daniels'  Comet  in  Cancer. 

In  like  manner,  I  obtained  nine  positions  of  the  comet,  the 
first  two  in  August,  in  the  San  Jacinto  Mountains,  about  a  hundred 
miles  southeast  of  Pasadena,  and  the  others  at  the  latter  place. 
To  the  last,  the  comet  was  visible  to  the  naked  eye;  but,  owing 
to  twilight,  opera-glasses  were  almost  always  used  in  identifying 
the  comparison  stars.  (L.  B.) 

84 


MOTION  OF  BRIGHT  COMETS 

These  observations  plotted  on  the  celestial  globe  (§51,  Ex.  4) 
bring  out  several  features  regarding  the  comet's  motion.  Its- 
path,  during  the  period  of  observation,  is  found  to  lie  entirely 
north  of  the  equator,  extending  in  a  direction  south  of  east,  over 
55°,  through  the  zodiacal  constellations,  Gemini,  Cancer,  and 
Leo.  There  is  slight  change  in  velocity,  though  at  the  beginning 
motion  is  rather  faster  than  at  the  end. 

The  coordinates  derived  from  the  first,  fifth  and  last  observa- 
tions, including  precession  (§  59)  are: 

1907,  Aug.  15d15h.7:  R.  A.,  6h  43m;  DecL,  +18°.0 
11  Sept.  6  16  .3:  R.  A.,  9  29;  DecL,  +13  .1 
"  Sept.  17  16  .5:  R.  A.,  10  24;  DecL,  +  7  .5 

The  whole  change,  therefore,  in  33  days  amounted  to  a 
little  over  3.5  hours  in  right  ascension,  and  in  declination 
to  about  10°,  showing  that  the  comet  was  moving  slowly, 
compared  with  the  moon  (§  58),  but  more  rapidly  than  Venus 
(§  83,  Obs.). 

Observations  like  these  are,  of  course,  not  in  the  same  class  as 
those  taken  by  astronomers  with  equatorial  telescope  and  filar 
micrometer.  In  order,  however,  to  obtain  some  standard  of 
comparison,  eight  positions  fixed  at  observatories  in  August  and 
September  are  plotted  on  the  globe,  and  the  corresponding  path 
for  the  comet  marked  out  with  heavy  thread  (§  57).  The  path 
laid  down  from  eye-estimates  is  then  seen  to  coincide  in  places 
with  this  ' 'observatory  path,"  and  at  most  deviates  from  it  only 
about  half  a  degree.  This  check  is  suited  only  to  elementary 
work,  but  it  shows  that  results  are  as  accurate  as  would  be  ex- 
pected from  observations  taken  by  the  eye,  aided  only  with  opera- 


73.  Color  and  brightness  of  celestial  objects. — To  distinguish 
even  marked  differences  in  the  color  and  brightness  of  celestial 
objects  requires  training.  At  first,  special  care  should  be  taken 
to  observe  only  under  favorable  conditions,  when  the  sky  is 
clear,  unaffected  by  twilight  or  moonlight,  and  the  objects  con- 

85 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

sidered  are  well  above  the  horizon.     Exercises  like  the  following 
may  serve  as  a  guide: 

1.  When  three  or  more  of  the  bright  planets  are  visible,  pick 
out,  if  possible,  one  that  is  clear  white  in  color,  one  tinged  with 
red,  and  one,  with  yellow. 

2.  Make  a  list  of  eight  or  ten  of  the  brightest  stars  seen  in  one 
evening,  and  examine  them  individually,  noting  which  are  clear 
white,  which  tinged  with  red,  and  which,  if  any,  with  yellow. 

3.  Should  a  bright  comet  be  visible,  note  the  color   of  its 
^nucleus. 

4.  Repeat  exercises  1  and  2  in  different  seasons,  if  practicable, 
so  as  to  bring  under  scrutiny  all  the  bright  planets,  and  all  stars 
of  the  first  magnitude,  visible  at  the  given  place. 

5.  When  as  many  as  three  bright  planets  are  visible,  estimate 
which  is  the  brightest,  which  ranks  second,  and  which   third. 
Note  also  their  relative  variation,  whether,  for  instance,  the  differ- 
ence between  Jupiter  and  Venus  is  greater  or  less  than  that  be- 
tween Jupiter  and  Saturn. 

6.  In  the  year  when  Mars  is  an  evening  star,  make  an  approxi- 
mate determination  of  its  varying  brightness,  using  each  time, 
if  possible,  a  red  star  for  comparison  (Byrd,  §  168). 

7.  Make  a  list  of  eight  or  ten  of  the  brightest  stars  seen  in 
^one  evening,  and  then  arrange  them  in  order  of  brightness. 

8.  When  Algol,  i.  e.,  /8  Persei,  is  of  maximum  brightness,  com- 
pare it  with  a  Persei,  and  taking  a  "step"  as  the  least  difference 
recognized  in  brightness,  estimate  whether  the  variation  between 
them  is  one  step  or  more  (Byrd,  §  205). 

9.  On  a  date  when  a  minimum  is  predicted  for  Algol  in  the 
evening,  compare  it  with  neighboring  stars,  three  or  four  times 
at  intervals  of  about  an  hour.     Select,  if  possible,  each  time  a 
star  that  Algol  just  matches  in  brightness,  or  if  that  is  impracti- 
cable, indicate  by  steps  the  relation  between  the  two   (Byrd, 
§  206). 

In  dealing  with  the  varying  brightness  of  any  object,  care 
should  be  taken  in  choosing  comparison  stars.  They  should 
not  be  near  brighter  stars  nor  differ  much  in  color  from  the  vari- 

86 


APPARENT  MOTION  OF  THE  STARS 

able.  It  is  also  important  for  the  comparison  star  to  have  about 
the  same  altitude  as  the  variable,  and  be  near  it  in  the  heavens, 
though  no  effort  is  to  be  made  to  look  at  both  at  the  same  '  ime. 

74.  Apparent  motion  of  the  stars. — A  single  night's  study  of 
the  heavens  suffices  to  show  that  the  stars  do  not  remain  fixed  in 
regard  to  the  horizon  or  other  circles  of  reference.  To  find  out 
the  law  that  governs  their  motion,  a  number  of  different  obser- 
vations should  be  taken.  It  is  well  to  include  simple  ones',  such 
as  watching  to  see  whether  stars  low  in  the  east  and  west  are 
rising  higher  or  sinking  lower,  and  whether  those  well  up  to  the 
south  and  north  are  moving  toward  the  eastern  or  western  quarter 
of  the  horizon.  Note  also  the  times  when  bright  stars  rise  or  set 
and  their  places  on  the  horizon.  If  the  principal  constellations 
have  been  grouped  in  reference  to  the  four  quarters  of  the  heavens 
in  different  seasons  (§  20,  Obs.),  compare  the  two  observations, 
and  see  what  changes  have  taken  place. 

The  following  are  often  included  among  the  more  formal  obser- 
vations made: 

EXERCISE  1. — On  an  evening  in  the  fall  and  again  in  the  spring, 
make  two  sketches  of  the  "great  dipper"  in  reference  to  the  hori- 
zon, with  an  interval  of  two  hours,  if  possible,  between  them 
(Byrd,  §  193). 

EXERCISE  2. — Twice  in  the  same  evening,  allowing  an  interval 
of  two  hours,  make  note  of  the  position  of  several  of  the  circum- 
polar  constellations  in  reference  to  the  North  Star  and  to  the 
cardinal  points. 

EXERCISE  3. — Twice  in  the  same  evening,  allowing  an  interval 
of  two  hours,  note  the  position  of  three  bright  constellations,  one 
chosen  near  the  eastern  horizon,  one  near  the  meridian,  and  the 
third  near  the  horizon  toward  the  west. 

Final  conclusions  should  be  formulated  as  fully  and  critically 
as  warranted  by  all  the  data  obtained. 

75.  Position  of  ecliptic  and  celestial  equator. — These  reference 
circles  are  marked  on  globes  and  star-maps,  and  if  the  individual 

87 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

stars  on  or  near  them  are  noted  and  carefully  identified  in  the 
sky,  the  circles  can  be  traced  out  there.  Of  course,  only  half 
the  celestial  sphere  is  visible  at  one  time,  but  if  two  observations 
are  taken  about  six  months  apart,  both  the  ecliptic  and  equator 
can  be  followed  throughout  their  course,  and  something  learned 
regarding  their  position  in  reference  to  the  horizon  of  the  par- 
ticular place. 

OBSERVATION. — S.  C.  0.,  Northampton,  Mass.,  8h  p.  M.,  E.  s. 
T.,  Wednesday,  April  1,  1908.  From  the  observing  roof  over 
the  laboratory  room,  I  locate  the  ecliptic  in  the  sky,  having  on  a 
previous  night  identified  the  stars  along  its  path.  Beginning 
near  the  eastern  horizon  I  trace  it, 

1.  Between  a  and  6  Virginis, 

2.  Below  and  parallel  to  77  0  Virginis, 

3.  Through  p  and  a  Leonis,  5  Cancri  and  6  Geminorum, 

4.  To  the  right  of  £  Tauri  by  about  J  f  0  Tauri,  and  a  trifle 
below  T  and  K  Tauri. 

The  ecliptic,  I  find,  intersects  the  horizon,  south  of  the  east 
point,  over  the  right-hand  end  of  College  Hall;  and  north  of  the 
west  point,  behind  the  left-hand  poplar  tree  in  the  foreground. 
Its  highest  point  is  reached  at  5  Cancri,  and  the  altitude  of  this 
star,  from  three  measures  made  with  jointed-rods  and  protrac- 
tor is  68°,  the  check  on  the  globe  giving  65°. 

I  noted  also  that  the  three  bright  planets  visible  were  close  to 
the  ecliptic,  Jupiter  near  its  highest  point  and  Mars  and  Venus 
rather  low  in  the  west. 

In  like  manner,  at  the  same  place,  on  the  same  date,  about  a 
quarter  of  an  hour  later,  I  trace  the  course  of  the  equator,  follow- 
ing it, 

1.  Through  f  and  TJ  Virginis,  barely 

2.  Below  a  Sextantis,  a  little 

3.  Above  i  and  r  Hydrse  and 

4.  Through  5  Monocerotis  and  5  Orionis. 

It  meets  the  horizon  in  the  east,  over  the  left-hand  end  of  Col- 
lege Hall;  and  in  the  west,  over  the  buildings  on  Hospital  Hill,  in 
the  distance,  or  just  to  the  left  of  the  large  elm  tree  in  the  fore- 

88 


THE  MILKY  WAY 

ground.  At  its  highest  point,  it  coincides  almost  exactly  with 
the  star,  r  Hydrse,  close  to  the  meridian  at  this  time;  and  having, 
according  to  my  measures,  an  altitude  of  48°.  The  theoretical 
check  gives  47°. 7,  if  r  is  assumed  to  be  just  on  the  meridian. 

(E.  H.) 

76.  Form,  position  and  motion  of  the  Milky  Way. — The  time 
to  observe  the  Milky  Way  is  when  the  sky  is  really  clear  and  there 
is  no  moon.  The  place  should  be  as  free  as  possible  from  the 
effect  of  artificial  light,  and  in  order  to  see  faint  outlying 
parts  of  the  stream,  the  eyes  should  be  kept  in  the  dark  a  little 
before  observing  begins.  If,  as  is  to  be  assumed,  the  constella- 
tions are  well  known,  no  lights  should  be  employed  till  at  the  end, 
when  numerical  estimates  are  made,  or  measures  taken  and 
other  notes  recorded.  To  follow  the  Milky  Way  throughout  its 
whole  circuit,  and  to  find  whether  it  changes  its  position  in  refer- 
ence to  the  observer's  horizon  will  require  two  or  more  observa- 
tions, in  different  seasons  of  the  year,  somewhat  like  the  following : 

OBSERVATION. — Sunday,  July  26,  1908,  Goshen,  Mass.  Pre- 
paratory to  observing  the  Milky  Way,  I  have  already  located  an 
approximate  north  and  south  line  on  a  large  stepping  stone 
(Byrd,  §  9,c);  and,  by  aligning  from  it,  fixed  the  west  point  on  the 
horizon.  A  suitable  resting  place  for  jointed-rods  has  been 
obtained  by  nailing  a  board  to  the  top  of  the  hitching  post  and 
leveling  it  up. 

Looking  at  the  sky  this  evening  between  half  after  nine  and  ten, 
I  find  the  arch  of  the  Milky  Way  spanning  the  heavens  in  the 
east,  meeting  the  horizon  near  the  north  and  south  points,  and 
where  it  is  highest  passing  close  to  /3  Cygni.  Its  course  is  traced 
from  the  lower  part  of  Scorpio  at  the  south,  up  through  the  upper 
part  of  Sagittarius,  through  Scutum,  Aquila  and  Cygnus,  and 
down  through  Lacerta  and  Cassiopeia  at  the  north.  In  Cygnus, 
the  main  stream  divides  into  two  branches,  the  smaller  one 
extending  into  Ophiuchus  with  Serpens  winding  its  way  between 
them.  The  brightest  as  well  as  the  widest  part  of  the  main  arch 
seems  to  be  in  Sagittarius  with  a  diameter  equal  to  the  star-line, 
ffy  Sagittarii  or  about  11°.  By  a  rough  eye-estimate,  I  make  the 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

altitude  of  the  highest  point  -f  of  the  distance  between  horizon 
and  zenith,  that  is,  79°.  The  mean  of  three  measures  with  jointed- 
rods  and  protractors  gives  71°.  As  a  whole,  I  find  the  Milky 
Way  an  irregular  stream  of  light,  with  a  diameter  by  turns  widen- 
ing and  narrowing.  The  branch,  especially,  is  irregular  in  con- 
tour, and  in  places  appears  more  like  patches  of  light  than  a 
continuous  stream.  (A.  M.  H.) 

Though  it  may  not  be  practicable  to  obtain  ideal  conditions 
for  the  Milky  Way,  it  should  not  be  altogether  neglected.  Some- 
thing of  it  can  be  seen  even  in  the  vicinity  of  electric  lights;  and 
if  its  intersections  with  the  horizon  are  fixed  approximately  on  a 
single  night,  a  clue  is  given  as  to  whether  the  arch  is  a  small  or  a 
great  circle. 

77.  Stars   and   nebulae  with  opera-glasses. — If   two    short 
periods  on  different  dates  are  given  to  this  topic,  the  working- 
list  (Byrd,  §  1)  should  include  the  star-clusters  of  the  Pleiades  and 
Coma  Berenicis,  the  nebulae  of  Andromeda  and  Orion,  and  a  few 
wide  doubles,  such  as  f  Ursse  Majoris  and  a  Capricorni  (§  84,  7). 
Whatever  object  is  examined,  the  aim  should  be  to  find  answers 
to  definite   questions.     For   example,   with   a    Capricorni,    see 
whether  the  components  are  equal  or  unequal  in  brightness,  alike 
or  unlike  in  color,  how  they  resemble  in  these  respects  the  com- 
ponents of  £  Ursse  Majoris,  and  how  the   distances  separating 
the  stars  of  the  two  doubles  compare  (Byrd,  §  204). 

It  should  be  borne  in  mind  that  the  main  object  in  observing 
heavenly  bodies  is  not  to  see  something  pretty,  but  to  find  out 
something. 

78.  Latitude  from  altitude  of  stars. — The  North  Star,   also 
called  Polaris,  is  the  star  to  employ  in  finding  latitude.     Were  it 
exactly  at  the  pole,  that  is,  if  its  declination  were  just  90°,  its  alti- 
tude observed  at  any  time  would  give  latitude  directly;  for  the 
altitude  of  the  pole  equals  the  latitude  of  the  place.     The  declina- 
tion of  Polaris  is,  however,  88°. 8,  so  that  when  it  crosses  the 
meridian  above  the  pole,  its  altitude  is  1°.2  greater  than  the 

90 


LATITUDE  FROM  POLARIS 


latitude,  but  when  it  crosses  below  the  pole,  its  altitude  is  smaller 
by  1°.2. 

Even  if  Polaris  is  not  on  the  meridian,  its  altitude  may  still  be 
utilized  in  finding  latitude;  for  the  difference  between  the  altitude 
of  pole  and  star  depends  upon  the  star's  hour-angle  at  the  time 
of  observation,  and  when  that  is  known,  the  required  correction 
can  be  taken  from  Table  IV  in  the  Ephemeris.  This  table,  now 
called  Table  I,  has  appeared  since  1911  in  an  extended  form, 
and  is  entered  with  two  arguments,  as  explained  in  the  introduc- 
tory paragraph. 

OBSERVATION. — Kansas  University,  Lawrence,  Tuesday,  Dec. 
22,  1908.  The  Circles  (§  12)  are  placed  approximately  in  the 
meridian  on  the  north  porch  of  the  physics'  building  to  measure 
the  altitude  of  Polaris.  The  base  is  leveled  with  a  carpenter's 
level,  and  a  little  before  six  in  the  evening,  four  readings  are 
taken  for  altitude,  two  with  the  vertical  circle  facing  east  and  two 
with  it  facing  west.  The  mean  value  for  the  angle  is  39°  47', 
and  the  mean  of  the  corresponding  times,  5h  52m,  c.  s.  T.,  or 
23h  35m  sidereal  time  (§  64,  Ex.).  When  observed,  the  star  was, 
therefore,  lh  51m  east  of  the  meridian  (Byrd,  §  39,  current  Ephem- 
eris, p.  595),  and  the  correction  opposite  this  hour-angle  in 
Table  IV  is  found  to  be,  —  1°  3',  which,  if  refraction  is  included, 
makes  the  required  latitude  38°  43'.  (El.  H.) 

The  following  is  a  concise  form  of  arrangement  for  the  numerical 
operations : 

TABLE  V. — LATITUDE  FROM  POLARIS. 


Stand.  T.  of  Obs. 
Stand. M.E.  of  Lawrence 

Mean  local  T.  of  Obs. 
Sidereal  T.  of  Obs. 

R.  A.  of  Polaris 
Hour-angle  of  Polaris 


5h  52m 
21 


5    31 
23    35 

1    26 


22      9 

(-1     51) 


Obs.  altitude 

Correc.  for  Refrac. 
Correc.  fr.  Table  IV 

Latitude  fr.  Obs. 


91 


+39°   47', 


-   1 


+38     43; 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

A  mean  value  for  latitude,  obtained  by  combining  this  deter- 
mination with  two  others,  made  within  the  hour  by  the  same 
observer  in  the  same  way  is  38°  52',  which  is  5'  less  than  the  true 
value  for  the  University  (§87,  Ex.  1). 

If  the  meridian  altitude  of  a  star  south  of  the  zenith  is  em- 
ployed for  latitude,  choose  one  that  is  bright  and  below  rather 
than  above  the  equator.  Neither  Antares  nor  Fomalhaut  is  too 
far  south  to  be  satisfactorily  observed  (Byrd,  §  1,  last  part). 
Instead  of  a  star,  a  bright  planet  may  be  used,  if  its  southing  is 
low  enough,  and  comes  at  a  convenient  time.  The  reduction, 
either  for  star  or  planet,  is  made  just  as  for  the  sun  in  Ex.  2,  §  44. 

79.  Adjusting  and  reading  a  sun-dial. — It  is  not  practicable 
to  give  directions  that  always  apply  in  adjusting  a  sun-dial. 
Much  depends  upon  its  precise  form,  and  the  place  where  it  is  to 
be  used.  Sometimes  also,  account  must  be  taken  of  the  season 
of  the  year;  for  the  time  during  which  a  dial,  fixed  on  a  window 
sill,  is  in  the  sunshine  varies  largely  from  month  to  month. 

If  the  essential  condition  is  met,  that  is,  if  the  dial  can  be  read 
at  sun  noon,  it  is  usually  satisfactory,  with  the  sun-dial  illustrated 
in  Fig.  11  (the  same  as  Fig.  3)  to  proceed  somewhat  as  follows: 

First  place  an  upright  with  heavy  base  and  movable  arm,  so 
that  a  plumb  line  suspended  from  the  latter  passes  through  the 
center  of  the  upper  part  of  the  style.  Just  under  the  point  of  the 
bob,  mark  a  dot,  and  later,  on  different  days  with  different 
plumb-bobs,  adjust  and  check  its  exact  position.  Then  connect 
the  mark  thus  fixed  with  the  center  of  the  style  where  it  joins  the 
base  of  the  dial,  and  the  line  drawn  gives  the  intersection  of  a 
plane  that  is  nearly  vertical,  and  passes  almost  exactly  through 
the  central  line  of  the  style. 

The  next  step  is  to  bring  this  line  into  the  plane  of  the  meridian. 
After  a  rough  adjustment  has  been  made,  shift  the  base  slightly 
east  or  west,  at  the  instant  of  sun  noon.  Several  trials  on  differ- 
ent days  may  be  required,  but  in  the  end  the  line  should  lie  in 
the  center  of  the  beam  of  sunlight  at  sun  noon.  Finally,  the 
sheet  of  paper,  graduated  to  hours  and  parts  of  an  hour,  for  the 

92 


SUN-DIAL  ADJUSTED 

latitude  of  the  place,  is  fastened  on  the  base,  with  its  noon  line 
coinciding  with  this  meridian  line. 

The  style  should  be  placed  accurately  at  the  proper  angle 
when  the  sun-dial  is  first  made,  but  sometimes  a  slight  cor- 
rection is  necessary.  In  that  case,  loosen  the  screws  on  the 


FIQ  11.— Open-Style  Sun-Dial. 

supporting  block,  and  crowd  a  small  wedge  between  the  block 
and  the  style,  either  at  the  bottom  or  top,  according  as  the 
angle  of  altitude  is  too  great  or  too  small.  In  making  this 
adjustment,  bear  in  mind  that  raising  the  style  makes  the  sun- 
dial time  slower  before,  but  faster  after,  sun  noon,  and  that 
just  at  this  instant  an  error  in  the  altitude  of  the  style  has  no 
-effect  upon  the  time. 

93 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

OBSERVATION.— N.  C.,  New  York,  N.  Y.,  Tuesday,  Sept.  2r 
1913.  The  sun-dial  employed  is  like  that  of  Fig.  11,  page  93, 
approximately  adjusted  according  to  the  preceding  directions.  It 
would  be  a  waste  of  time  to  make  a  very  critical  adjustment,  for 
the  instrument  is  a  rough,  first  model,  with  imperfect  gradua- 
tions, and  doubtless  an  error  in  the  altitude  of  the  style. 

The  readings  taken  from  watch  and  dial  are: 

Sun-dial.  Watch. 

12h  35m  0s  12h  31m  42s 

In  order  to  compare  these  two  times,  they  must  be  alike,  i.  e.r 
both  apparent  or  both  standard.  The  sun-dial  time  is,  as  usual,, 
reduced  to  standard,  thus, 

Sun  time,  12h      35m     O1 

Equation  of  time,  — 19 


Local  mean  time,  12        34      41 

Stand.  Merid.  W.  of  N.  Y.,  4        9 


Stand,  time  fr.  Obs.,  12        30      32 

Stand,  time  fr.  watch,  12         31       42 


Error  of  watch  by  Obs.,  - 1       10 

Since  the  true  error  of  the  watch,  according  to  the  standard 
clock  of  the  Western  Union  Time  Service  was  57s  fast,  to  the 
nearest  second,  the  error  of  the  sun-dial  was,  +13".  Two  other 
readings  taken  between  twelve  and  one  o'clock  made  the  error 
of  dial  time,  +98  and,  +128. 

80.  Diurnal  paths  charted. — A  number  of  diurnal  paths  can 
be  brought  into  small  compass,  in  convenient  form  for  comparison 
by  plotting  them  on  rectangular  paper.  As  an  illustration  a  series 
of  actual  observations  is  taken.  All  were  made  with  the  same  in- 
strument, the  Circles  (§12),  and  in  the  same  manner  (§30).  Other 
details,  including  place  and  date  are  given  in  the  following  table : 

94 


DIURNAL  PATHS  CHARTED 


TABLE  VI. — DIURNAL  PATHS,  S.  C.  (X,  NORTHAMPTON,  MASS.,  1908-19091. 


DATE  OF  OBS. 

DESIGNATION 

OP  PATH. 

DECLINATION 
OF  BODY. 

OBS.  MER. 
ALTITUDE. 

INITIALS  OF 
OBSERVER. 

1908 

March  24 

Sun,  Si  Si 

+  1°.5 

49°.  0 

F,  J.  D. 

March  24 

Venus,  W 

+18.4 

M.  E.  J. 

April  24 

Sun,  S,Si 

+12.9 

61  .2 

H.  B. 

June  17 

Sun,  S,S, 

+23.4 

71  .0 

E.  H. 

Sept.  21 

Sun,  8484 

+  0.7 

48.9 

E.  C.  M. 

Nov.  16 

Sun,  S*Si 

-18.8 

28.6 

E.  C.  M. 

Dec.  21 

Sun,  S.S. 

-23.5 

24.0 

K.  K. 

1909 

May  26 

Moon,  MM 

+14.9 

63.2 

A.  H. 

(on  Merid.) 

All  points  obtained  for  the  eight  paths  are  plotted  in  Fig,  12, 
from  measures  of  altitude  and  azimuth,  contained  in  the  original 
notes.  The  reference  lines  employed  are  a  section  of  the  hori- 
zon, the  heavy  line  near  the  bottom,  with  E  and  W.  marking 
the  east  and  west  points;  and  that  part  of  the  celestial  meridian 
between  the  zenith  and  the  south  point.  Note,  that  SZ,  SE, 
and  SW.  are  equal  each  to  each,  as  each  is  the  projection  of  the 
quadrant  of  a  great  circle.  To  show  how  any  individual  point 
is  located,  let  it  be  required  to  fix  the  position  of  Venus  when  its 
altitude  is  41°.l  and  azimuth  78°.4,  a  degree  according  to  the 
scale  taken,  being  equal  to  £  of  a  division  of  the  rectangular 
paper  used.  The  number  of  divisions  corresponding  to  the  given 
altitude  and  azimuth  are  then  f  of  the  number  of  degrees  in 
these  coordinates,  or  32. Od  and  61. Od,  respectively.  Now,  as 
azimuth  is  reckoned  along  the  horizon  from  the  south  point 
toward  the  west,  61.0d  are  counted  off  from  S  toward  W  on  the 
horizon  line,  and  then  32.0d  laid  off  vertically  above  this  point 
locates  the  planet  near  the  upper  V  hi  the  diagram. 

Fig.  12  and  the  table  above  give  a  general  idea  of  the  amount 
and  character  of  the  observing  that  should  be  undertaken  for 
diurnal  paths,  though  no  special  significance  attaches  to  the 
dates  for  Venus  and  the  moon,  and  any  bright  planet  may  be 
taken  though  Venus  and  Mars  are  especially  interesting  (§  83). 

95 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

In  the  dates  for  the  six  solar  paths,  there  will  inevitably  be  large 
variations,  and  the  individual  observer  is  fortunate  if  one  of 
them  comes  near  an  equinox  and  another  near  one  of  the 
solstices  (§  31).  The  large  number  obtained  at  or  near  such  times, 
in  the  series  considered,  is  due  mainly  to  the  fact  that  different 
paths  were  traced  by  different  observers. 

It  is  well,  as  here,  to  obtain  for  every  path,  when  practicable, 


FIG.  12. — Diurnal  Paths  of  Sun,  Moon,  and  Venus. 

the  critical  point  near  the  meridian,  since  examination  of  diagram 
and  globe  shows  that,  if  one  point  only  is  fixed,  this  gives  the 
most  satisfactory  key  to  the  path  for  the  day.  It  is  also  the  one 
most  readily  checked,  for  declination  subtracted  from  observed 
altitude  gives  in  each  instance  the  approximate  meridian  altitude 
of  the  celestial  equator  at  the  place  of  observation  (§  28).  Thus, 
from  columns  three  and  four  of  the  table,  the  value  derived  for 
the  meridian  altitude  of  the  equator  is  47°. 8,  as  against  the  true 

96 


SMALL  TELESCOPE  TESTED 

value  47°. 7,  and  from  the  mean,  the  largest  deviation  is  five- 
tenths  of  a  degree.  The  value  for  latitude  found  from  this  alti- 
tude of  the  equator  is,  of  course,  as  accurate  as  the  altitude. 

When  five  or  more  points  have  been  fixed  for  the  path  of  any 
one  body,  its  course  is  marked,  as  in  the  figure,  by  a  smooth  curve, 
and  the  deviation  of  an  individual  point  from  the  curve  gives  a 
test  of  the  accuracy  of  its  altitude  and  azimuth.  Even  for  iso- 
lated points,  an  approximate  check  is  obtained  by  a  careful 
scrutiny  of  all  the  data,  and  when  a  path  is  indicated  by  two  or 
three  points,  the  eye  following  the  general  direction  of  adjacent 
curves  gains  a  fair  notion  of  the  path  as  a  whole. 

A  simple  diagram  of  diurnal  paths  stands  for  many  and  labori- 
ous observations,  and  when  it  is  completed  it  deserves  thorough 
study.  The  following  points  especially  should  receive  attention : 

1.  Relation  between  changes  in  noon  altitude  and  sunset  point. 

2.  Connection  between  position  and  extent  of  solar  paths  and 
seasons  of  the  year. 

3.  Connection  between  position  and  extent  of  any  path,  and 
declination  of  the  body. 

4.  Likeness  or  unlikeness  of  paths  for  different  bodies. 
Considerations  of  this  character  should  also  be  supplemented 

by  exercises  with  the  celestial  globe,  especially  such  as  show  how 
portions  of  diurnal  paths  on  one  side  of  the  meridian  compare 
with  those  on  the  other,  and  whether  any  given  path  is  part  of  a 
small  or  a  great  circle. 

81.  Magnifying  power  of  small  telescope  and  quality  of  object- 
glass. — A  simple  method  for  determining  the  magnifying  power 
of  a  telescope  consists  in  dividing  the  diameter  of  the  object-glass 
by  that  of  the  small  circle  of  light,  which  is  seen  close  to  the  eye- 
piece, when  the  glass  is  turned  toward  the  sky  in  the  daytime. 
This  circle  is,  in  reality,  the  image  of  the  objective  aperture  di- 
minished in  the  same  proportion  as  the  telescope  magnifies.  Its 
diameter  may  be  determined  by  Berthon's  Dynamometer,  or  by 
almost  any  form  of  scale  when  a  high  degree  of  precision  is  not 
required.  (See  "Campbell's  Practical  Astronomy,"  §  150). 

97 

7 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

EXERCISE  1.— Eraser  Hall,  K.  U.,  Tuesday,  July  13,  1909. 
Having  adjusted  the  portable  transit-instrument,  approximately 
for  stellar  focus,  I  take  three  measures  of  the  diameter  of  the  ob- 
jective by  laying  a  common  foot-rule  on  the  cell  and  aligning 
downward  by  the  eye.  With  a  home-made  scale  (Byrd,  §  20,  c), 
I  measure  also  the  "circle  of  light"  three  times. 

Like  tests  are  applied  on  two  other  days  of  the  same  week,  and 
the  mean  of  ten  measures  for  each  diameter  is  found  to  be  1.90 
in.,  for  the  objective,  and  0.14  in.  for  the  circle,  which  gives  13.6 
diameters  as  the  magnifying  power  of  the  instrument  with  the 
diagonal  eye-piece.  (El.  H.) 

The  efficiency  of  a  telescope  depends  largely  upon  the  quality 
of  the  object-glass.  It  ought  to  show  stars  like  points  of  light, 
and  all  images  sharp  and  clear-cut  without  " wings  of  light"  or 
extraneous  color. 

Irradiation,  or  the  so-called  wing  of  light,  on  one  side  of  a 
bright  object,  usually  indicates  that  all  parts  of  the  objective 
have  not  the  same  refractive  power;  blurred  images  indicate 
spherical  aberration,  that  is,  light  from  a  single  point  in  the 
object  has  not  all  been  brought  to  the  same  point  in  the  image; 
and  images  of  variegated  color  indicate  chromatic  aberration, 
that  is,  light  rays  of  different  color  have  not  all  been  brought  to 
the  same  focus. 

With  a  home-made  telescope,  a  wing  of  light  sometimes 
appears  which  is  caused  by  inaccurate  centering  of  the  different 
lenses. 

EXERCISE  2.— K.  U.,  Saturday,  July  10,  1909.  In  testing  the 
objective  of  the  portable  transit  instrument,  Jupiter  is  first 
brought  into  the  field  of  view,  and  the  eye-piece  carefully  focused. 
No  wings  of  light  are  seen,  the  outline  of  the  planet  is  sharply 
defined,  and  two  satellites  are  visible.  To  test  for  chromatic 
aberration,  I  draw  out  the  eye-piece  a  little,  and  find  a  fringe  of 
light  green  at  the  upper  part  of  the  disk.  When  the  eye-piece 
is  pushed  in,  there  is  seen,  on  the  upper  limb  to  the  right,  a  pale 
fringe  of  different  colors,  but  it  is  far  less  distinct  than  that  first 
mentioned. 

98 


SMALL  TELESCOPE  TESTED 

Two  stars  are  examined  in  testing  for  spherical  aberration. 
First,  I  obtain  a  sharp  image  of  the  second  magnitude  star,  0 
Leonis,  and  note  that  a  slight  inward  motion  of  the  eye-piece  has 
no  effect,  but  when  it  is  drawn  out  the  star  is  not  quite  so  sharp. 
Then,  with  €  Virginis,  a  third  magnitude  star,  in  good  focus,  I  try 
the  effect  of  a  cap  placed  over  the  objective  and  covering  half 
its  diameter.  I  find  that  the  star  image  remains  as  sharp  as  at 
first,  but  is,  of  course,  diminished  in  brightness.  (El.  H.) 

The  objects  observed  were  rather  low  when  these  tests  were 
made,  which,  perhaps,  accounts  for  the  fact  that  results  do  not 
agree  more  closely  with  those  required  by  theory  for  a  fully 
satisfactory  instrument. 

Many  helpful  details  connected  with  the  adjustment  and  use 
of  a  small  telescope  are  given  by  Proctor  in  his  "Half -Hours  with 
the  Telescope." 


CHAPTER  VII. 

PARTIAL  SOLAR  ECLIPSE;  PATHS  OF  PLANETS;  PLANETS  AND  STARS  WITH 
SMALL  TELESCOPE;  GENERAL  PROBLEM  OF  TIME  WITH  TRANSIT  IN- 
STRUMENT; TIME  FROM  TRANSIT  INSTRUMENT;  LONGITUDE  FROM  TIME. 

82.  Partial  solar  eclipse. — Astronomers  attach  little  impor- 
tance to  any  eclipse  except  a  total  one  of  the  sun.  Nevertheless, 
in  an  elementary  course  in  astronomy,  all  eclipses,  whether  of 
the  sun  or  the  moon,  deserve  careful  study.  This  is  especially 
true  of  a  solar  eclipse,  for  even  the  partial  phase  is  not  often 
visible  in  any  one  locality. 

The  mechanical  appliances  for  observing  should  include  card- 
patterns  for  drawing  circles,  some  instrument  for  measuring 
the  sun's  altitude,  a  number  of  spectacles  with  glass  of  varying 
shades  suited  to  different  phases  of  the  eclipse,  and  opera-glasses 
or  small  telescope.  The  eye-piece  of  the  latter  must  be  carefully 
protected  (§  69),  and  all  watches  employed  compared  with  a 
correct  time-piece.  The  main  points  to  be  considered  may  be 
arranged  in  a  scheme  something  like  the  following : 

Points  Connected  with  Beginning  of  Eclipse. 

1.  A  little  before  first  contact,  make  note  of  the  sun's  altitude, 
and  record  whether  or  not  the  sky  is  free  from  haze  and  clouds, 
especially  near  the  sun. 

2.  Draw  a  circle  for  the  solar   disk,  indicating  which  is  the 
east  and  which  the  west  limb. 

3.  Record  the  time  of  first  contact,  that  is,  the  instant  when 
the  limb  of  the  sun  is  first  indented. 

4.  Locate  the  point  where  the  eclipse  begins  by  a  mark  on  the 
circle  representing  the  solar  disk. 

5.  During  the  ten  or  fifteen  minutes  following  first  contact, 
.show  the  progress  of  the  eclipse  by  drawing  on  the  solar  circle 

100 


PARTIAL  SOLAR 


several  arcs  which  mark  the  boundary  between  the  eclipsed  and 
uneclipsed  portions.  Include  also  a  record  of  the  times  corre- 
sponding to  the  arcs. 

Points  Connected  with  Maximum  Phase. 

6.  As  the  time  predicted  for  this  phase  approaches,  indicate 
the  progress  of  the  eclipse  as  in  5,  passing  to  a  second  solar 
circle,  as  soon  as  the  eclipsed  portion  begins  clearly  to  diminish. 

7.  Estimate  what  proportion  of  the  solar  circumference  is  in- 
dented, and  how  far  in  the  indentation   extends,  expressed  in 
terms  of  the  sun's  diameter. 

8.  Describe  the  general  appearance  of  the  sun,  noting  whether 
the  moon's  limb  can  be  followed  beyond  the  solar  disk. 

9.  Note  whether  the  sun's  light  at  this  time  shows  any  pecu- 
liarity. 

10.  Examine  and  describe  the  images  of  the  sun  seen  under 
trees  or  shrubs  (§42). 

11.  Look  at  the  sun  with  opera-glasses  or  small  telescope,  and, 
if  any  spot  is  visible,  locate  it  on  one  of  the  solar  circles. 

12.  Describe  points  of  difference  between  the  view  given  by 
the  telescope  and  that  observed  directly. 

13.  See  if  any  bright  star  or  planet  is  visible  with    opera- 


Fio.  13. 


Points  connected  with  the  end  of  the  eclipse  are  so  similar  to 
those  considered  at  its  beginning  that  one  outline,  with  slight 
modifications,  serves  for  both.  The  diagrams  in  Fig.  13  show 

101 


FI113T  OBSEvlVATTONS  IN  ASTRONOMY 

the  solar  disk  when  one-tenth  and  six-tenths  of  its  diameter  are 
eclipsed,  and  give  an  idea  of  the  illustrations  desired,  though  for 
the  note-book,  the  scale  ought  to  be  larger.  Any  scheme  that 
is  to  be  used  as  a  guide  should,  of  course,  be  studied  before  the 
eclipse  begins. 

83.  Paths  of  planets  among  the  stars. — Two  of  the  bright 
planets,  Jupiter  and  Saturn,  move  so  slowly  that  during  a  period 
of  several  months  only  short  sections  of  their  paths  can  be  ob- 
tained. Venus  and  Mars  on  the  other  hand  move  so  rapidly, 
and  are  so  bright  that  in  seasons  when  they  are  favorably  placed 
for  observing,  it  is  not  difficult  to  trace  their  course  in  the  con- 
stellations through  60  or  70  degrees  (Byrd,  §  171).  Mercury, 
on  account  of  its  nearness  to  the  sun,  is  not  often  seen  at  the 
same  time  with  the  stars.  To  identify  it  and  fix  two  or  three 
points  in  its  path  on  the  sphere,  measures  may  be  made  of  its 
altitude  and  azimuth  when  it  is  visible  in  bright  twilight  (§51, 
Ex.  1).  This  is  a  method  applicable  also  to  the  other  planets; 
but  for  them  it  is  best  to  make  a  series  of  sketches  on  different 
nights,  fixing  positions  in  reference  to  comparison  stars  by  careful 
estimates  of  distance  and  angle  (§59). 

In  checking  and  combining  such  sketches  and  in  making  de- 
ductions from  them,  no  mechanical  appliance  equals  the  celes- 
tial globe,  but  to  facilitate  the  work  of  a  whole  class,  and  to 
assure  for  each  member  a  permanent  record,  it  is  well  to  prepare 
a  special  map  on  heavy  cardboard,  much  larger  in  scale  than  the 
small  uranographies.  Let  it  contain,  as  far  as  practicable,  the 
usual  reference  circles,  including  sections  of  the  equator  and 
ecliptic,  and  all  stars  used  by  the  class  with  others  needed  to 
give  a  good  representation  of  that  portion  of  the  heavens  ob- 
served. All  who  have  taken  part  in  the  observations  enter,  then, 
in  their  note-books  a  tracing-paper  copy  of  this  map,  and  fix  on 
it  with  precision  the  different  points  determined  by  the  indi- 
vidual data  obtained.  A  smooth  curve  drawn  through  the  points 
shows  at  a  glance  the  path  of  the  planet  watched  in  the  sky 
from  night  to  night. 

102 


PATH  OF  VENUS  AMONG  THE  STARS 

The  following  observations  of  Venus  illustrate  a  number  of 
details,  though  it  will  not  often  be  practicable  for  an  individual 
student  to  obtain  so  many  positions.  Eight  or  ten  is  a  fair 
number. 

OBSERVATION. — Whitin  Observatory,  Wellesley  College,  Welles- 
ley,  Mass.  During  the  spring  of  1908,  I  located  30  points  in  the 
path  of  Venus  among  the  stars.  Neither  mechanical  nor  optical 
aids  were  employed,  except  that  a  marine  glass  was  used  on 
three  nights  in  identifying  comparison  stars.  In  several  in- 
stances, observations  followed  on  successive  nights,  but  two  or 
three  days  was  the  usual  interval,  All  but  three  were  taken 
here  and  those  were  obtained  in  Boston.  (M.  W.  D.) 

The  30  points  mentioned  above  are  fixed  by  dots  in  Fig.  14, 
on  the  following  page.  The  numbers  near  them  indicate  the 
order  in  time,  and  the  curve  drawn  through  them  shows  the 
path  traced  for  Venus.  It  is  seen  to  lie  north  of  the  ecliptic 
but  always  near  it,  and  to  extend  eastward  through  the  zodiacal 
constellations,  Aries,  Taurus,  and  Gemini,  passing  near  the 
Pleiades.  In  order  to  ascertain  its  extent  in  degrees  and  for 
other  deductions,  recourse  must  be  had  to  the  celestial  globe. 
From  the  plot  made  there,  the  entire  length  of  the  path  during 
the  85  days  between  the  first  and  last  observations  measures 
70°.  As  required  by  theory,  the  rate  of  motion  in  this  path 
varies  largely;  for  the  planet  passed  over  11°. 5  during  the  first 
ten  days,  but  only  over  3°. 5  during  the  last  ten,  which  includes 
the  position  marked  stationary  in  the  almanacs.  The  coordi- 
nates of  the  first  and  last  positions  and  the  declination  of  "far- 
thest north"  were  obtained  from  the  globe,  and  the  results  with 
the  corresponding  values  from  the  Ephemeris  are : 

Date.  R.  A.  fr.  Obs.,    fr.  Ephem.;     Decl.  fr.  Obs.,     fr.  Ephem- 

March  21,  7h.8        2h  38m  2h  42*,  +  16°.3         +  17°.3 

(Farthest  north)    +26  .5  +27  .0 

June  13,      9 .0        7  35  7  35  ,  +22  .5         +22  .5 

It  follows,  therefore,  that  during  the  period  of  observation, 
Venus  moved  east  about  5  hours  in  right  ascension,  but  in 

103 


PATH  OF  VENUS  AMONG  THE  STARS 

declination  motion  was  in  opposite  directions,  first  north  10°, 
then  south  4°,  reckoning  to  the  nearest  degree.  To  fix  the  point 
farthest  north,  the  planet's  path  is  marked  out  as  usual  by  pass- 
ing a  fine  cord,  stiff  with  wax,  as  symmetrically  as  possible  with 
regard  to  the  points  plotted  on  the  globe  (§  57).  Examination 
then  shows  that  the  greatest  declination  of  Venus  is,  +26°.5, 
but  during  two  weeks,  from  April  26  to  May  10,  there  is  no 
measurable  change  in  declination,  though  meanwhile  right  ascen- 
sion increases  nearly  an  hour.  This  constancy  of  declination  is, 
however,  not  surprising,  as  later  it  is  found  that  its  value,  ac- 
cording to  the  Ephemeris  varies,  during  the  interval,  less  than 
0°.4.  And  the  best  naked-eye  observations  are  likely  to  be  in 
error  one  or  two-tenths  of  a  degree,  and  globe  checking  is  cer- 
tainly less  accurate. 

The  globe  makes  it  practicable  to  find  approximately  the 
greatest  eastern  elongation  of  Venus,  that  is,  its  greatest  angular 
distance  from  the  sun  during  the  synodic  period  involved.  Any 
measure  of  the  distance  between  the  positions  fixed  for  the  sun 
and  planet  on  the  same  date,  gives  the  angle  of  elongation,  and 
to  find  when  it  is  greatest,  it  is  only  necessary  to  make  a  number 
of  measures.  The  value  obtained  April  13,  is  45°. 3,  before  that, 
less,  between  this  date  and  April  26,  there  is  no  perceptible 
change,  but  after  that  it  grows  less  again.  The  angle  given  in 
the  Ephemeris  for  greatest  elongation  is  45°. 6  on  April  26;  but 
the  uncertainty  about  the  date  from  the  globe  plot  does  not 
signify  poor  observing  nor  any  unusual  inaccuracy  in  the  globe. 
Reference  to  the  Ephemeris  shows  that  between  April  13  and 
26,  the  planet  gains  in  right  ascension  9m.2  on  the  sun  but  loses 
2°  27'  in  declination.  Therefore,  since  the  relative  change  in 
coordinates  is  small,  nearly  equal  and  in  opposite  directions,  the 
angular  distance  between  the  two  bodies  cannot  change  largely. 
Calculation  gives  an  increase  of  half  a  degree  between  the  dates 
mentioned  (Byrd,  §  72). 

84.  Planets,  nebulae,  and  stars  with  small   telescope. — In 

making  the  first  observation  of  these  objects  with  the  telescope, 

105 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

attention  should  center  on  simple  definite  points  like  those  given 
in  the  working  list  below: 

1.  Examine  Venus  near  inferior  conjunction   when  it  shows 
the  crescent  phase.    Compare  it  as  regards  form,  size,  and  color 
with  the  new  moon  seen  directly,  without  magnifying  power. 

2.  See  whether  the  telescope  affects  the  color  of  Mars,  and 
whether  it  shows  a  disk  for  the  planet. 

3.  Observe  Jupiter  twice  in  the  same  evening,  and  make,  each 
time,  a  diagram  showing  the  position  of  the  satellites.    Describe 
the  belts  if  they  are  visible. 

4.  Look  at  Saturn  and  note  whether  or  not  the  appearance  of 
the  rings  is  like  that  which  Galileo  obtained  with  his  telescope. 

5.  Examine  the   nebulae  of  Andromeda   and  Orion  and  see 
how  they  differ  in  size,  form,  and  brightness. 

6.  Describe  the  appearance  of  three  of   the  following  star- 
clusters  : 

The  Pleiades:   Praesepe  in  Cancer;   Coma  Berenicis;    H.  VI; 
33,  34,  near  r\  Persei;  M.  13,  between  r/  and  $  Herculis. 

While  making  observations,  keep  in  mind  points  like  these: 

(1)  Difference  between  opera-glass  (§  77)  and  telescopic  views. 

(2)  Density  and  form  of  cluster,  and  size  in  terms  of  the  field 
of  view. 

(3)  Approximate  number  of  stars  by  count  or  estimate. 

(4)  Tendency  to  cluster  in  any  noticeable  way. 

(5)  Range  in  magnitude  of  stars  and  contrasts  in  color. 

7.  Examine  about  half  the  double  stars  in  the  list  below: 

(1)  r  Ursae  Maj.,  i.  e.,  (8)  ft  Cygni. 

Mizar  and  Alcor.  (9)  61  Cygni. 

(2)  aCapricorni.  (10)  £  Piscium. 

(3)  cLyrse.  (11)  6  Serpentis. 

(4)  0  Lyrae.  (12)  f  Ursae  Maj.,  i.  e. 

(5)  v  Draconis.  Mizar. 

(6)  6  Orionis.  (13)  a  Geminorum. 

(7)  6  Orionis.  (14)  7  Virginis. 

106 


GENERAL  PROBLEM  OF  TIME 

8.  Make  a  diagram  of  the  telescopic  field  showing  Mizar  and 
-Alcor,  the  neighboring  eighth  magnitude  star,  and  the  compo- 
nents of  Mizar. 

The  first  two  stars  of  the  list  are  very  wide  doubles,  called 
sometimes  naked-eye  doubles,  and  the  components  of  €  Lyrse, 
though  nearer  together,  are  still  widely  separated.  Let  the  dis- 
tance between  the  components  of  these  three  be  estimated  in 
terms  of  the  field  of  view,  and  the  brightness  of  the  other  two 
compared  with  Mizar  and  Alcor.  For  the  closer  doubles,  Mizar 
itself  serves  well  for  a  standard,  both  as  regards  the  distance  and 
the  brightness  of  the  two  stars.  In  addition  to  the  comparison 
of  each  double  star  with  a  given  pair,  taken  as  a  standard,  note 
the  color  and  relative  magnitude  of  the  components  of  each  pair. 

85.  General  problem  of  time  with  transit  instrument. — It  is 
not  a  very  difficult  undertaking  to  find  time  from  observations 
made  with  a  transit  instrument  placed  in  the  meridian,  if  a 
few  astronomical  formulae  are  accepted  without  demonstration 
(§  86).  Were  the  instrument  perfect  and  perfectly  adjusted,  a 
single  perfect  record  of  the  transit  of  one  star  across  one  thread 
would  give  directly  the  time  sought,  that  is  the  error  of  the 
sidereal  clock;  for  it  would  be  simply  the  difference  between  the 
record  of  the  clock  and  the  right  ascension  of  the  star  (§  49). 

Since,  however,  these  ideal  conditions  are  never  realized,  at 
least  four  stars  should  be  observed  over  as  many  as  three  threads; 
and  account  taken  of  the  errors  in  level,  azimuth,  and  collima- 
tion.  The  mean  of  the  times  on  the  different  threads  is,  then,  the 
time  of  observation,  and  according  to  Mayer's  formula  (" Corn- 
stock's  Field  Ast.,"  §  75,  (149)  ),  the  transit  of  each  star  gives 
an  equation  of  the  form, 

a-  T  = 

where  a  is  the  right  ascension  of  the  star,  T  its  sidereal  time  of 
transit,  AT  the  approximate  clock  error,  and  the  other  three 
terms  the  corrections  for  the  errors  just  mentioned.  In  these 
terms  the  capital  letters,  A,  B,  and  C  signify  the  factors  that 

107 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

are  constant  for  a  given  star  at  a  given  place.     Their  values  in 
terms  of  latitude  and  declination  are, 


cos  5      '  cos  5      '  cos  5* 

At  any  place  where  a  transit  instrument  is  in  routine  use  for 
determining  time,  it  is  customary  to  compute  these  factors  for 
different  values  of  declination,  and  arrange  them  in  tables, 
called  ABC  Tables. 

The  small  letters  signify  instrumental  errors.  The  error  in 
azimuth,  a,  is  the  angular  deviation  of  the  rotation  axis  from 
due  west,  plus  when  the  deviation  is  south,  minus  when  north. 
The  error  in  level,  6,  is  the  angular  deviation  of  the  rotation 
axis  from  the  plane  of  the  horizon,  plus  when  the  west  end  of 
the  axis  is  high,  minus  when  low.  The  error  of  collimation,  c, 
is  the  angular  deviation  of  the  standard  sight-line  from  the 
collimation  axis.  Both  of  these  lines  pass  through  the  so-called 
"optical  center"  of  the  object-glass,  but  the  axis  of  collimation 
is  that  which  is  perpendicular  to  the  rotation  axis,  and  the  sight- 
line  is  defined  as  that  which  passes  through  the  standard  thread, 
real  or  imaginary,  the  former  being  usually  the  middle  thread 
and  the  latter  the  mean  of  the  threads.  The  sign  of  c  is  plus 
when  the  sight-line,  from  thread  to  objective,  intersects  the  celes- 
tial sphere  to  the  east  of  the  collimation  axis.  It  follows,  there- 
fore, that  when  the  rotation  axis  is  reversed,  i.  e.,  turned  end 
for  end,  the  sign  of  c  is  changed.  Hence,  to  obtain  well  bal- 
anced data,  it  is  usual  to  observe  an  even  number  of  stars,  half 
with  one  position  of  the  rotation  axis  and  half  with  the  other. 

In  actually  recording  the  transits,  it  is  by  no  means  necessary 
to  employ  a  sidereal  time-piece.  With  home-made  appliances,  a 
watch  set  to  standard  time  is  often  more  convenient  (§  88). 

The  instrument  used  in  obtaining  the  set  of  star  transits  given 
in  the  following  section  is  like  that  described  in  §  10,  and  illus- 
trated in  Fig.  15  which  is  the  same  as  Fig.  1.  The  diameter  of  the 
object-glass  is  1.5  inches  and  the  magnifying  power  30  (§81). 
Instead  of  spider  threads,  fine,  black  silk  threads  are  inserted 

108 


GENERAL  PROBLEM  OF  TIME 

in  the  negative  eye-piece.  They  present  the  appearance  of  heavy 
bars,  do  not  require  much  light,  and  so  make  it  possible  to 
observe  sixth  magnitude  stars,  though  the  fifth  is  a  preferable 
limit.  The  rotation  axis  has  neither  clamp  nor  setting  circle. 


Fia.  15. — Home-Made  Transit  Instrument. 

The  two  positions  of  the  axis  may  be  designated  by  the  numbers 
I  and  II,  according  as  the  end  marked  I  or  II  is  to  the  east. 
The  telescope  is  held  in  any  desired  position  by  means  of  a 
counterpoise  which  is  merely  a  narrow  bag  of  bird-shot  fitted 
tightly  around  the  tube  near  the  lower  end  of  the  dew  cap.  To 

109 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

facilitate  "settings,"  that  is,  the  pointing  at  individual  stars,, 
eight  or  ten  so-called  decimation  lines  are  drawn  along  the  rota- 
tion axis  at  either  end.  Each  one  was  made  to  coincide  with 
the  heavy  reference  line  on  the  inner  face  of  the  east  wye, 
when  a  carefully  identified  star  was  in  the  center  of  the  field 
of  view,  and  its  declination  marked  on  the  line.  Hence,  it 
follows  that  to  bring  a  star  into  the  field,  it  is  only  necessary,  a 
little  before  its  time  of  transit,  to  turn  the  telescope  until  the 
declination  line  of  the  star  coincides  with  the  line  of  reference 
just  mentioned.  For  stars  that  have  no  declination  lines, 
settings  are  made  by  interpolating.  Changes  in  level  that  shift 
the  reference  line  interfere  somewhat  with  this  method ;  but,  as 
with  any  transit  instrument,  the  star's  magnitude  and  time  of 
meridian  transit  aid  in  identifying  it. 

A  numerical  evaluation  of  the  level  error  is  impracticable,  but 
the  rotation  axis  is  carefully  adjusted  by  placing,  under  one  end 
or  the  other,  pieces  of  thin  pasteboard  made  to  fit  the  wyes,  and 
testing  with  the  striding  level.  A  difference  in  one  thickness  of 
paper  is  easily  detected,  and  it  is  not  difficult  to  reduce  the 
level  error  practically  to  zero,  considering  the  standard  of  accu- 
racy required  with  an  instrument  of  this  character.  In  making 
the  reduction  of  observations,  therefore,  the  term  Bb  is  dropped 
from  Mayer's  formula. 

A  set  of  eight  stars,  taken  half  before  and  half  after  reversal, 
usually  gives  a  fair  determination  of  the  collimation  error,  but 
that  for  azimuth  is  more  troublesome,  as  it  is  difficult  to  reverse 
the  instrument  without  changing  its  value. 

86.  Time  with  home-made  transit  instrument. — The  only 
problem  to  be  considered  here,  and  that  rather  beyond  the  scope 
of  the  book,  is  to  find  the  error  of  a  common  watch  with  the 
simplest  appliances. 

OBSERVATION. — W.  V.,  Lawrence,  Kan.,  Saturday,  Oct.  30, 
1909.  Two  sets  of  eight  stars  each  are  observed  with  the  instru- 
ment described  in  the  preceding  section.  On  its  base,  well 
lighted  by  a  lantern  near  it,  an  Elgin  watch  is  placed  in  a  cush- 
ioned box.  The  observer,  following  the  star  across  the  field, 

110 


TIME  WITH  TRANSIT  INSTRUMENT 


looks  down  as  it  disappears  behind  each  of  the  three  bars,  and 
notes  time,  a  crude  method  of  recording  which  naturally  intro- 
duces rather  large  accidental  errors.  On  this  date,  the  moon 
being  not  far  from  full,  gives  all  needed  illumination  for  the  field 
of  view  (§  10). 

The  working  list  for  this  observation  consists  of  a  number  of 
stars  and  their  coordinates  taken  from  the  Ephemeris.  All  are 
included  that  are  available  during  several  hours,  as  far  as  they 
meet  the  necessary  conditions  of  brightness  and  position. 

The  principal  data  for  the  first  set  of  stars  are  given  in  the 
following  table: 

TABLE  VII.— TIME  SET,  SATURDAY,  OCT.  30,  1909,  W.  V.,  LAWRENCE,  KAN. 


STARS,  Pos.  I. 

DECL. 

EQUATIONS. 

AT's. 

11  Cephei 

+70°  54' 

-lm508.5=AT-1.6a-3.1c 

-Im358.3 

a  Aquarii 

-  0  46 

-1    41.8=A!T+0.6a-1.0c 

-1    38  .4 

7  Aquarii 

-  1   51 

-1    38.6=A77+0.7a-1.0c 

-1    35  .4 

TT  Aquarii 

+  0   55 

-1    37.8=A!T+0.6a-1.0c 

-1    34  .4 

STARS,  Pos.  II. 

77  Aquarii 

-  0   35 

-1    28.2=AT+0.6a+1.0c 

-1    33  .2 

T  Pegasi 

+10  22 

-1    28.8=A!T+0.5a+1.0c 

-1    33  .7 

t   Cephei 

+65   44 

-1    26.3=A77-l.la+2.4c 

-1    34  .9 

a  Pegasi 

+14  43 

-1    31.3=A3rt+0.4a+1.0c 

-1    36  .1 

To  obtain  the  equations  in  the  third  column  of  the  table, 
numerical  values  are  substituted  in  Mayer's  formula,  the  term 
bB  having  been  dropped,  as  already  explained  (§  85).  First,  the 
star's  right  ascension,  which  is  its  sidereal  time  of  transit 
(§  49),  is  reduced  to  local  mean  time  (Byrd,  §  53),  and  then  to 
standard  time  by  applying  a  correction  of  21m  12s,  the  best 
known  value  of  the  longitude  from  the  standard  meridian  (§87, 
Ex.  2,  6).  The  difference  between  this  theoretical  time  of 
transit,  and  that  observed  with  the  watch  keeping  standard 
time  gives  its  approximate  error,  a—  T.  This  constitutes  the 
first  member  of  the  equation,  and  the  minus  sign  before  it 
indicates  that  the  watch  is  fast  (§36). 

Ill 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

The  second  member  contains  the  corrections  that  are  required 
in  finding  the  true  watch  error,  and  here  A  and  C,  the  coeffi- 
cients of  a  and  c  have  been  replaced  by  their  values  taken  from 
ABC  Tables.  There  too  the  signs  are  given,  and  C  is  found 
positive  for  all  the  stars  of  the  set,  but  it  is  known  that  the 
collimation  error,  c  has  opposite  signs  for  positions  I  and  II 
(§85),  and  so,  for  one  position  or  the  other,  Cc  must  be  negative. 
When  the  solution  has  been  completed,  a  positive  c  simply  means 
that  the  signs  of  Cc,  i.  e.,  of  c  were  entered  correctly  at  first,  a 
negative  value,  that  the  signs  taken  must  be  reversed  in  giving 
the  collimation  error  for  the  particular  position  of  the  instrument. 

After  the  eight  equations  have  been  formed  in  this  manner,  the 
problem  is  to  derive  the  watch  error  AT7,  and  a  and  c,  the  instru- 
mental errors.  The  discussion  of  the  theory  of  reduction  cannot 
be  taken  up  here,  but  it  must  be  noted  that  the  unknown  quan- 
tities are  not  to  be  treated  exactly  like  x,  y,  and  z  in  the  common 
algebraic  equation.  The  solution  may  be  carried  out  as  follows,* 
where  the  equation  marked  p  is  that  derived  from  the  north 
star  or  polar,  and  that  marked  m  is  obtained  by  taking  the  mean 
of  the  three  equations,  based  upon  the  time  stars : 

-  lm  50".5  =  A  T- 1.6  a-  3.1  c  (p) 
-1  39.4  =  AT+0.6a-1.0c(w) 
-0  11.1=  +2.2a+2.1c(n=m-p) 

—  1  42  .4  =  AT  -  1.6  c  (mi  =  m  with  q  substituted) 

For  Pos.  II  the  equations  obtained  in  like  manner  are: 

-lm268.3=A7T-l.la+2.4c(pO 
-1  29.4=A!F+0.5a+1.0c(wO 
-0  3.1=  -fl.6a-1.4c(w') 
-0  1.9=  -f  a- 0.9  c  (q') 
-I  28.  4  =  AT  4-1.4 c(wi') 

"The  writer  learned  about  this  particular  form  of  reduction  from  Dr.  T.  H. 
Safford,  for  many  years  Professor  of  Astronomy  at  William's  College,  and,  as 
far  as  known,  it  was  original  with  him. 

112 


TIME  WITH  TRANSIT  INSTRUMENT 

To  find  the  unknown  quantities,  solve  first  for  c.  Its  value 
derived  from  q  and  q',  the  equations  containing  a  and  c,  is  38.6, 
from  the  equations  containing  AT  and  c,  48.7,  making  the  mean 
value,  4fl.2,  negative  for  Pos.  I.  By  substituting  this  value  for 
c  in  q  and  qf,  and  taking  the  mean,  a  is  found  to  be  +  ls.4;  and 
a  like  substitution  in  m\,  and  m\  gives  the  mean  AT,  —  lm 
358.0  at  8h  10m,  the  mean  of  the  times  of  the  different  star 
transits.  The  values  of  AT  for  each  star,  given  in  the  last  col- 
umn of  the  time-set  table,  are  obtained  by  substituting  c  and  a  in 
the  eight  equations.  As  already  noted,  the  method  of  recording 
probably  affected  especially  these  individual  errors,  but  the  fact 
that  their  mean  for  Pos.  I  is  larger  than  for  Pos.  II  indicates  the 
need  of  a  further  correction  for  collimation.  Refinements  of  this 
kind,  however,  belong  rather  to  instruments  of  precision  than  to 
the  rude,  ten-dollar  make-shift  which  is  here  considered. 

The  second  set  of  eight  stars  is  reduced  like  the  first,  and 
gives  the  value  of  AT,  -lm  328.0  at  10h  9m,  making  the  mean 
of  the  two  errors,  -  lm  338.5  at  9h  10m,  the  mean  of  the  times 
of  the  two  sets.  A  little  later  at  9h  30m,  the  watch  is  compared 
by  telephone  with  the  clock  of  A.  Marks,  a  Lawrence  jeweler, 
who  courteously  took  pains  to  have  standard  time  correct  to 
the  nearest  second.  Several  signals  were  given  and  the  final 
result  made  the  watch  fast,  lm  348.5.  While  this  error  is  not 
to  be  regarded  as  absolutely  correct  at  the  time  of  comparison, 
and  a  change  may  have  taken  place  in  the  watch  during  20m, 
it  is  probable,  all  things  considered,  that  the  determination  of 
time  from  the  16  stars  was  correct  within  a  second. 

87.  Latitude  and  longitude  without  observation. — These  geo- 
graphical coordinates  may  be  obtained  from  maps,  more  or  less 
accurately,  depending  on  the  scale  of  the  map  and  its  degree  of 
accuracy. 

EXERCISE  1. — Given  the  latitude  and  longitude  of  the  State 
University,  Lawrence,  Kan.,  +38°  57'.2  and  6h  20m  588  W. 
(Appendix);  required  to  find  from  a  map  the  latitude  and 
longitude  of  Ft.  Riley,  Kan. 

113 

8 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

The  map  employed  is  "King's  Grammar  School  Geography," 
used  in  the  schools  of  the  state  (1910),  and  having  a  scale  of 
26  miles  to  the  inch.  With  strips  of  rectangular  paper,  I  make 
three  mesaures  of  the  distance  by  which  Ft.  Riley  is  north  of 
Lawrence  and  the  same  number  of  its  distance  west.  The 
means  of  the  linear  distances,  reduced  to  degree  measure  for 
this  part  of  the  map,  makes  the  fort  5'.5  north  of  Lawrence  and 
5m  25s  west.  So,  according  to  this  determination,  its  latitude 
is,  +39°  2'.7  and  longitude  6h  26m  23s  W.  |(C.  J.  W.) 

The  values  given  by  the  Commandant  of  the  Post  are,  latitude, 
+39°  3'.8  and  longitude,  6h  27m  9s  W. 

If  the  distances  involved  are  small,  the  required  coordinates 
may  be  found  by  counting  "sections"  when  practicable,  for  a 
section  is  exactly  a  square  mile  in  those  parts  of  the  country 
where  land  is  laid  out  regularly  in  sections  and  ranges. 

EXERCISE  2. — Taking  the  latitude  and  longitude  of  the  State 
University  given  in  Exercise  1,  find  by  the  aid  of  section  lines  the 
latitude  and  longitude  of  Wide  View. 

(a)  By   reckoning   the   sections   in   the   farms    between    the 
university  and  the  given  place,  the  latter  is  located  three  miles 
west,  and  three-quarters  of  a  mile  south  of  the  university  sta- 
tion.    The  problem,  then,  is  to  reduce  miles  to  degrees.     Now, 
a  degree  of  longitude  in  linear  measure  decreases   rapidly  as 
distances  from  the  equator  increase,  but  a  degree  of  latitude 
increases  slightly.    For  this  place,  as  the  distance  considered  is 
small,  it  is  sufficiently  accurate  to  take  69  miles  equal  to  one 
degree  of  latitude,  and  hence  three-fourths  of  a  mile  equals  39//. 
This  subtracted  from  the  latitude  of  the  university,  +38°  57' 15" 
makes  that  of  Wide  View,  +38°  56'.6.     In  the  locality  consid- 
ered, the  value  of  one  degree  of  longitude  used  in  the  survey  of 
public  lands,  carried  far  enough  for  this  exercise,  is  53.87  miles. 
Therefore,  three  miles  equals  0°.056  or  138.4,  making  the  longitude 
of  Wide  View,  6h21mll8.4. 

(b)  In  this  exercise,  more  accurate  results  are  derived  from  a 
critical  sectional  map  of  the  vicinity  of  Lawrence,  which  is  avail- 
able, since  it  includes  both  the  university  buildings  and  the 

114 


LONGITUDE  FROM  OBSERVATION 

house  at  Wide  View.  Careful  measures  with  rectangular  paper 
place  this  house  0.75  miles  south  of  the  university  station,  a 
value  agreeing  with  that  found  above  (Byrd,  §  5),  but  the  dis- 
tance west  is  3.18  miles,  which  according  to  the  method  employed 
in  a,  equals  0°.059  or  14s.  16. 

It  follows  that  the  required  coordinates,  obtained  for  Wide 
View,  by  subtracting  39"  from  the  latitude  of  the  university 
and  adding  14B  to  its  longitude  are, 

Latitude,  +38°  56'.6  and  longitude,  6h  21m  12s  W. 

While  this  method  gives  no  warrant  for  claiming  that  tenths 
of  seconds  are  known,  the  value  found  for  the  longitude  of  Wide 
View  is  doubtless  correct  to  the  nearest  half  second  of  time. 

88.  Longitude  from  time  determinations. — To  deal  intelli- 
gently with  the  actual  determination  of  longitude,  it  is  essential 
to  have  a  clear  idea  of  just  what  longitude  is.  Young  defines  it 
as  "the  angle  at  the  pole  of  the  earth  between  the  standard 
meridian  and  the  meridian  passing  through  the  place"  (Young, 
Art.  61).  This  angle  is  measured  by  the  arc  intercepted  on  the 
equator,  and  that,  in  turn  by  the  time  required  for  a  star  or  the 
mean  sun  (Byrd,  §  37)  to  pass  over  the  arc. 

Since  the  meridian  of  Greenwich  is  commonly  taken  as  the 
standard  or  zero  meridian,  all  points  for  example,  where  the  sun 
marks  noon  an  hour  later  than  at  Greenwich  are  said  to  be  in 
longitude  one  hour  west  of  Greenwich.  The  problem  of  finding 
the  longitude  of  any  place,  therefore,  consists  in  obtaining  the 
local  time  at  the  place,  and  then,  for  that  instant,  ascertaining 
the  corresponding  Greenwich  time.  The  latter,  however,  is  not 
often  one  of  the  stations  directly  employed,  as  the  older  ob- 
servatories in  any  country,  whose  longitude  from  Greenwich  is 
accurately  known,  serve  as  standards  of  reference. 

For  example,  let  A  be  on  the  zero  meridian,  B,  a  station 
whose  longitude  from  A  is  known,  and  C,  the  place  whose 
longitude  is  required.  The  local  time  at  C  compared  with  that 
at  B  gives  the  difference  in  longitude  between  C  and  B,  and 
C's  longitude  from  A  is  then  found  by  simple  addition  or  sub- 

115 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

traction,  according  as  B  is  west  or  east  of  A ;  for  west  longitudes 
are  reckoned  plus  and  east,  minus. 

EXERCISE. — From  the  determination  of  local  time  at  Wide  View, 
Lawrence,  Kan.,  required  to  find  approximately  the  longitude 
of  the  station. 

The  error  of  the  Elgin  watch  employed  was  ascertained  on 
three  dates,  Sept.  11,  25,  and  Oct.  30,  the  day  of  the  week  in 
each  case  being  Saturday,  so  that  comparison  could  be  made 
in  the  evening  with  jeweler's  time  in  town. 

To  illustrate  the  method  of  procedure,  the  October  observa- 
tions are  taken.  They  are  the  same  that  have  been  discussed  in 
§  86,  but  here  the  treatment  is  different,  for  in  the  present  prob- 
lem, longitude  instead  of  being  given,  as  before,  is  the  quantity 
to  be  determined.  Reference  to  the  original  notes  for  this  date 
shows  that  longitude  was  then  really  unknown,  but  that  the 
Ephemeris  time  of  transit  was  reduced  by  a  provisional  longitude, 
21m  8s,  to  approximate  standard  time,  and  that  the  watch 
showed  on  its  face  the  same  kind  of  time. 

While  this  is  the  convenient  way  to  use  a  watch  in  observing, 
in  the  subsequent  reductions,  it  is  desirable  to  deal  only  with 
local  time.  This  is  readily  effected,  for  the  times  to  be  consid- 
ered are  simply  the  two  times  of  star  transit,  that  derived  from 
the  Ephemeris  and  that  obtained  by  observation.  The  first  is 
expressed  in  local  time  by  the  mere  omission  of  the  correction 
for  longitude,  in  making  the  reduction  from  sidereal  time ;  and  the 
local  time  of  transit  is  found  without  tampering  with  the  hands 
of  the  watch,  for  it  matters  not  at  all  whether  they  are  set  back 
a  certain  number  of  minutes  and  seconds  before  observations  are 
taken,  or  whether  afterward,  this  interval  is  subtracted  from  the 
recorded  time  of  transit. 

Therefore,  to  find  the  first  member,  a—  T  of  each  fundamental 
equation,  take,  for  example,  11  Cephei  of  the  first  set,  Oct.  30. 
Its  local  time  of  transit  from  the  right  ascension  of  the  Ephemeris 
is  7h  5m  45s. 5  (§  49),  its  standard  time  of  transit,  actually  re- 
corded is  7h  28m  48s,  but  the  corresponding  local  time,  obtained 
,by  subtracting  the  correction  used  for  longitude,  21m  8",  is 

116 


LONGITUDE  FROM  OBSERVATION 

7h  7m  40s,  and  the  difference  between  these  two  times,  i.  e.t 
—  lm  54S.5  gives  the  required,  a—  T.  In  the  same  way  a—  T  is 
derived  for  the  other  stars,  and  the  solution  of  the  two  sets  of 
observations  carried  out  from  this  point  as  in  §  86  makes  the 
error  of  local  mean  time,  -  lm  398.0  at  7h  49m,  and,  -lm  368.0  at 
9h  48m,  or  if  means  are  taken,  the  watch  error  is,  —  lm  378.5  at 
8h  48m. 

This  determination  of  local  mean  time  constitutes  the  first 
and  most  laborious  part  of  the  work  demanded  in  finding  longi- 
tude. Theoretically  considered,  the  next  step  is  to  compare  the 
time-piece  of  Wide  View  with  a  clock  at  some  station  where 
longitude  has  been  accurately  determined,  for  the  difference  in 
the  longitude  between  two  stations  is  the  difference  in  their 
local  times.  So  far,  no  mention  has  been  made  of  a  second  sta- 
tion, and  indeed  no  one  in  particular  is  required.  The  one  thing 
necessary  is  to  make  a  comparison  with  a  clock  which  keeps 
correctly  the  time  of  a  meridian  at  a  known  distance  from 
Greenwich.  But  this  is  precisely  what  is  done  by  any  clock 
keeping  correct  standard  time;  for  standard  time  is  the  local 
time  of  the  standard  meridian  (§  22),  and  all  standard  meridians 
are  separated  from  Greenwich  by  a  known  number  of  hours. 

In  the  present  exercise  local  time  at  Wide  View  was  compared 
with  the  local  time  of  the  90th  meridian,  i.  e.,  with  standard  time 
in  the  time  section  of  the  place.  The  actual  comparison  was 
effected  between  the  watch  used  at  Wide  View  and  the  clock  of  a 
Lawrence  jeweler  set  to  standard,  that  is  90th  meridian  time. 
Instead  of  telegraphing  as  in  a  regular  longitude  "campaign," 
the  telephone  was  employed,  though,  of  course,  several  signals 
were  given. 

The  mean  of  the  corresponding  readings  with  watch  error  is: 

Local  time  Error  of  Elgin  Local  time 

at  Wide  View.          Watch  at  8h  48m.  of  90th  Meridian. 

9h  9m  568.5  -  lm  378.5  9h  29m  30* 

Since  it  is  impracticable  to  ascertain  the  watch  error  for  the 
exact  minute  of  comparison,  it  seems  more  reasonable  to  assume 

117 


FIRST  OBSERVATIONS  IN  ASTRONOMY 

that  it  is  constant  between  8h  48m  and  9h  10m  than  to  apply  a 
correction  for  rate,  as  is  usual  with  the  clock  of  an  observatory. 
The  corrected  local  time  at  Wide  View  is,  then,  9h  9m  568.5 
-Im378.5  or  9h8m198.0,  and  this  subtracted  from  the  90th 
meridian  time,  9h  29m  30s  gives  21m  11s  as  the  difference  in  longi- 
tude between  the  two  meridians.  And  finally,  since  the  meridian, 
with  which  comparison  is  made,  is  90°  west  of  Greenwich,  the 
longitude  of  Wide  View,  according  to  this  observation,  is 
6h21mll8  W. 

The  principal  data  for  the  three  nights,  when  observations 
were  taken  for  longitude,  are  given  in  the  following  table,  where 
W.  V.  and  W.  V.  T.  stand,  respectively,  for  Wide  View  and 
Wide  View  time. 

TABLE  VIII. — LONGITUDE  OF  WIDE  VIEW. 


No.  OP 

WATCH 

COMPARISON  OF  TIME- 

DATE  OP  OBS. 

STARS. 

ERROR  PR. 
OBS.  AT 
W.V. 

PIE 

CES. 

90th  M.  T. 
-  W.  V.  T. 

W.V. 

JEWELER'S 

WATCH. 

CLOCK. 

1909. 

Sept.  lld    9h.7 

Sept.  25      7  .5 
Sept.  25     13  .0 

8 

8 
8 

+0m508.5 

8h53ml8.5 
9   20  24  .0 

9h  15m  08.0 
9   40     0.0 

+21m88.0 
12  .8 

-1    35  .9 
-1     37  .8 

10  .2 

16 

-1     36.8 

Oct.  30       7  .8 

8 

-1     39  .0 

Oct.  30      9  .8 

8 

-1     36  .0 

9     9  56  .5 

9  29    30.0 

11  .0 

8  .8 

16 

-1     37.  5 

The  values  in  the  final  column  are,  of  course,  obtained  as 
above  by  correcting  the  watch  time  for  its  error,  and  then  taking 
the  difference  between  the  corrected  local  time  at  Wide  View, 
and  the  90th-meridian  time  of  the  jeweler's  clock.  The  mean 
of  the  three  nights  taken  directly  is  21m  10".  6.  If,  as  seems  rea- 

118 


LONGITUDE  FROM  OBSERVATION 

sonable,  each  night  is  weighted  according  to  the  number  of  stars 
observed  (Byrd,  §  4)  the  mean  obtained  is,  21m  11M,  and  this 
makes  the  whole  longitude  of  Wide  View,  west  of  Greenwich, 
6h  21m  11s,  a  value,  a  second  smaller  than  that  derived  in  b  of 
the  preceding  section. 

Another  determination  of  the  longitude  of  this  station  has 
been  made  from  the  occultation  of  five  stars  by  the  moon;  and 
though  the  work  involved  is  incomparably  greater,  the  final  result, 
6h  21m  15s,  is  less  accurate  than  that  above,  based  on  the  de- 
termination of  local  time.  The  latter  is  certainly  the  method  to 
be  preferred  by  amateurs,  depending  upon  simple  appliances. 


119 


APPENDIX. 


Latitudes  and  Longitudes  of  Places   for    Illustrative    Exercises 


Place.  Latitude. 

Ann  Arbor,  Mich.  +42°  16'.8 

Arequipa,  Peru  —16  24 

Baltimore,  Md.  +39   17  .5 

Boston,  Mass.  +42  21 .5 

Charlottesville,  Va.  +38     2 .0 

Cleveland,  Ohio  +41   30.1 

Columbia,  Mo.  +38  56  .9 

Denver,  Colo.  +39  40  .6 

Ft.  Riley,  Kan.  +39     3  .8 

Galveston,  Tex.  +29   18  .3 

Greenwich,  Eng.  +51   28  .6 

Hartford,  Conn.  +41   45.6 

Key  West,  Fla.  +24  33  .4 

Lawrence,  Kan.  +38  57  .2 

Montreal,  Canada  +45  30  .3 

Nashville,  Tenn.  +36     8  .9 

New  Orleans,  La.  +29  57  .8 

New  York,  N.  Y.  +40  48  .6 
NewYork,N.Y.,N.Col.+40  46 

Northfield,  Minn.  +44  27  .7 

Northampton,  Mass.  +42   19  .0 

Omaha,  Neb.  +41   15  .7 

Oxford,  Miss.  +34  22  .2 

Philadelphia,  Pa.  +39  57  .1 

Portland,  Me.  +43  37  .4 

Portland,  Ore.  +45  32 

Raleigh,  N.  C.  +35  47 

Salt  Lake  City,  Utah  +40  46.1 

San  Francisco,  Calif .  +37  47.5 

Santa  Fe,  N.  M.  +35  41  .1 

Savannah,  Ga.  +32     4  .9 

South  Hadley,  Mass.  +42   15.3 

Washington,  D.  C.  +38  55  .2 

Wellesley,  Mass.  +42   17  .7 


Longitude. 

+5h  34m 

55s 

+4 

45 

30 

+5 

6 

27 

+4 

44 

15 

+5 

14 

5 

+5 

26 

49 

+6 

9 

18 

+6 

59 

48 

+6 

27 

9 

+6 

19 

10 

0 

0 

0 

+4 

50 

42 

+5 

27 

14 

+6 

20 

58 

+4 

54 

19 

+5 

47 

12 

+6 

0 

14 

+4 

55 

50 

+4 

55 

51 

+6 

12 

36 

+4 

50 

33 

+6 

23 

43 

+5 

58 

7 

+5 

0 

38 

+4 

40 

50 

+8 

10 

9 

+5 

15 

2 

+7 

27 

35 

+8 

9 

43 

+7 

4.1 

+5 

24 

22 

+4 

50 

20 

+5 

8 

16 

+4 

45 

18 

120 

Authority 

American  Ephemeris 
American  Ephemeris 
U.  S.  Geological  Survey 
American  Navigator 
American  Ephemeris 
U.  S.  Geological  Survey 
American  Ephemeris 
American  Ephemeris 
Commandant  at  Ft.  Riley 
American  Navigator 
American  Ephemeris 
U.  S.  Geological  Survey 
American  Navigator 
U.  S.  Geological  Survey 
American  Ephemeris 
American  Ephemeris 
American  Navigator 
American  Ephemeris 
U.  S.  Geographical  Survey. 
American  Ephemeris 
American  Ephemeris 
Encyclopaedia  Britannica 
American  Ephemeris 
American  Ephemeris 
U.  S.  Geological  Survey 
Smithsonian  Meteor'l  Tables 
Encyclopaedia  Britannica 
U.  S.  Geological  Survey 
American  Ephemeris 
Loomis  Pract.  Astronomy 
American  Navigator 
American  Ephemeris 
American  Ephemeris 
American  Ephemeris 


INDEX. 


(All  references  are  to  sections,  not  to  paga.) 


ABC  Tables,  85. 
Algol,  varying  brightness,  73,  8,  9. 
Almanac,  Farmer's,  14,  25. 
Jayne's,  14,  24. 

Use  of,   in  observing,   32,   45;  in 
reductions,  19,  30,  32,  38,  Ex. 
5,  44,  Ex.  2,  50,  Ex.  1. 
See  also  Ephemeris. 
Altazimuth,  see  Circles. 
Altitude,  defined,  15,  10;  checked,  28, 

29,  30;  plotted,  51,  Ex.  1,  80. 
Observed,  of  equator  and  ecliptic, 
75;  of  Milky  Way,  76;  of  sun, 
19,  30,  31,  43;  of  stars,  78;  of 
moon,  planet,  sun,  80. 
See  also  Angles,  Latitude. 
Angles,   calculated  for  sun-dial,   13; 
estimated  in  sky,  33,  57,  Obs., 
59,  Obs.  2,  72,  Obs.  2;  plotted  on 
globe,  51,  Ex.  4;  read  from  pro- 
tractor, 31. 

See  also  Attitude,  Latitude. 
Angular  distance,  estimated  directly, 

56,  76;  by  star  lines,  46,  Obs., 

57,  Obs.,  59,  60,  72,  Obs.  2,  76. 
Measured  on  globe,  51,  57,  59,  67, 

83. 

Amplitude,  defined,  15, 13,  estimated, 
of  moon,  56. 

Apparent   noon,    defined,   22;   globe 
oriented  for,  40;  important  ob- 
servations at,  19;  standard  time 
of,  38,  Ex.  5. 
See  also  Apparent  time,  Time. 


Apparent  time,  defined,  22;  changed 
to  local  mean,  37;  to  standard, 
38,  Ex.  5. 
From   observation,    61,   Obs.,   62, 

Obs.  1,  79. 
See  also  Apparent  noon,  Time. 

Appliances,  miscellaneous,  14. 

Aquila,  principal  stars  identified,  33. 

Azimuth,  defined,  15,  12,  checked  on 
globe,  29,  51,  Ex.  2;  on  plotting 
paper,  80;  observed,  of  sun,  19, 
30,  31,  of  moon,  planet,  sun,  80. 

Brightness  of  celestial  objects,  71,  73. 

Cardinal  points  defined,  15,  22. 

Carpenter's  level,  adapted  to  transit 
instrument,  10;  used,  with  gno- 
mon, 14;  with  Circles,  30. 

Celestial  globe,  described,  26;  ori- 
ented, 40;  places  verified,  of  sun, 
40;  of  stars,  51,  Ex.  3. 
Used,  in  checking  observed  posi- 
tions, 29,  51;  in  deriving  coordi- 
nates of  observed  body,  51,  57, 
59,  83;  in  illustrating  diurnal 
paths,  80;  in  tracing  path  among 
the  stars,  of  comet,  72;  of  moon, 
57;  of  planet,  83;  of  sun,  41. 

Celestial  equator,  defined,  15,  15; 
marked,  on  globe,  26;  on  star- 
maps,  21;  traced  in  sky,  75; 
intersections  with  horizon,  75. 


121 


INDEX 


Celestial  sphere,  defined,  15,  1;  poles 
of,  15,  14',  represented  by  celes- 
tial globe,  26. 

Checks,  see  individual  terms,  as 
Altitude,  Declination,  Latitude. 

Circles,  described,  12;  adjusted,  30; 
used  in  measuring  altitude  and 
azimuth,  30,  78,  80. 

Circles  of  declination,  defined,  15,  17. 

Civil  and  astronomical  days,  35. 

Comets,  directions,  for  observing,  72; 

for  plotting,  39,  51,  Ex.  4. 
Daniel's  comet,  color,  brightness, 
72,  Obs.  1;  path  among  the  stars, 
observed,  72,  Obs.  2;  plotted  on 
globe,  51,  Ex.  4. 

Halley's  comet,  coordinates  by 
interpolating,  50,  Ex.  3;  plotted 
on  Proctor's  Atlas,  39,  Ex.  3. 

Color  of  celestial  objects,  73. 

Conjunction  of  planets,  60. 

Constellations,  identified  and  grouped, 
20;  mapped  from  sky,  33;  moon 
placed  in,  46;  motion  of,  74; 
path  of  MilkyWay  through,  76. 

Coordinates  defined,  15,  83. 
See  also  individual  terms. 

Day,  civil  and  astronomical,  35; 
mean  solar  and  sidereal,  defined, 
63;  length  compared,  63. 

Declination,  defined,  15,  28;  given  in 
small  almanac,  25;  used  hi  check- 
ing altitude,  28;  in  finding  lati- 
tude, 44,  Ex.  2,  Ex.  3,  78. 
See  also  Right  Ascension. 

Declination  of  zenith,  27. 

Definitions,  preliminary,  15. 

Diurnal  paths,  charted,  80;  critical 
points  in,  19,  30,  56;  illustrated 
with  globe,  80;  times  for  locating, 
lunar,  56;  solar,  31. 


Observed,  of  moon,  56,  80;  of  sun, 
18,  19,  30,  31,  80;  of  Venus,  80. 
Double  stars,  with  opera-glasses,  77; 
with  small  telescope,  84,  7,  8. 

East  and  west,  cardinal  points,  15, 
22}  direction  of,  on  map  and 
globe,  26. 

Eclipses,  lunar,  70;  solar,  82. 
Times  of  lunar  phases,  34,  66. 

Ecliptic,   defined,   15,    25;    marked, 
on  globe,  26;  traced  in  sky,  75; 
intersections  with  horizon,  75. 
Obliquity,   defined,    15,   28;   from 
observation,  44. 

Elongation,  greatest,  of  Venus,  83. 

Ephemeris,  American  and  Nautical 
Almanac,  described,  34,  day  em- 
ployed, 35;  interpolating  from, 
50,  Ex.  2. 

Used,  in  changing  apparent  to  mean 
time,  37;  in  checking  right  as- 
cension and  declination,  51,  Ex. 
1,  57,  59,  83;  in  finding  latitude, 
44,  78;  for  planetary  phenomena, 
32,  83;  for  verifying,  times  of 
eclipse,  66;  phases  of  moon,  65; 
positions  of  sun  and  star  on  globe, 
40,  Ex.,  51,  Ex.  3. 
Appendix,  Tables  II,  III,  34;  Table 
I  or  IV,  78. 

Equation  of  time,  defined,  36;  given 
in  almanacs,  24,  25,  34;  ap- 
plied, 37,  38,  Ex.  5,  40,  61,  Obs.; 
sign  for,  37. 

Equinoxes,  defined,  15,  26;  observa- 
tions at,  31,  44. 

Equipment,  1,  3-14. 

Error  of  time-piece,  determined,  61, 
62,  79,  86;  signs  for,  36. 


122 


INDEX 


Field  of  view,  diameter,  with  opera- 
glasses,  67;  with  small  telescope, 
68;  lighting,  62,  Obs.  2,  86; 
threads,  85. 

Focusing,  opera-glasses,  53,  55,  67; 
telescope,  53. 

Gnomon,  described,  and  adjusted,  5. 
Used  for  latitude,  43,  44;  for  north 
and  south  line,  61;  for  time,  61, 
Obs. 

Graduations,  for  Circles,  12;  for  sun- 
dial, 13;  how  read,  19. 

Greenwich  meridian,  phenomena  for, 
34;  standard  or  zero  meridian,  88. 

Greenwich  time,  changed  to  local  and 
standard,  rules,  48;  examples,  50, 
Exs.,  2,  3,  65,  66. 

Horizon,  sensible,  15,  5;  visible,  15,  4. 
Hour-angle,  defined,  15,  24,  of  sun, 

22;   of   vernal  equinox,    49;   of 

North  Star,  78. 
Hour-circles,  defined,  15,  17,  19;  on 

globe,  26;  on  star-maps,  21. 

Identification,  of  bright  planets,  32; 
of  constellations,  20,  46;  of  satel- 
lites, 34;  of  lunar  markings,  55, 
69;  of  stars,  33,  41,  46. 

Independence  in  observing,  16,  20, 
33. 

Interpolating  between  almanac  val- 
ues, 50. 

Instruments,  home-made,  5,  7,  10,  11, 
12,  13;  miscellaneous,  14;  prac- 
tice with,  31,  67. 
See  also  individual  names. 

Jointed-rods,  described,  11,  used  in 
measuring  altitude  and  azimuth, 
19,  75,  76. 


Jupiter,  appearance  in  small  telescope, 
84, 3;  comparative  brightness,  73, 
6;  diagrams  for  satellites,  34; 
located  among  the  stars,  59; 
used  in  testing  objective,  81. 

Latitude,  equal  declination  of  zenith, 

27;  obtained  from  maps,  87. 
From  observation,  of  sun,  44;  of 
stars,  78;  of  several  bodies,  80. 

Latitudes  of  places  mentioned  in  the 
text,  Appendix. 

Light-gathering  power  of  telescope,  54. 

Local  mean  time,  defined,  22;  equal 
standard,  22;  globe  oriented  for, 
40. 

Reduced  to  apparent,  37;  to  Green- 
wich, 48;  to  standard,  38;  from 
sidereal,  64,  Ex. 

Longitude,  celestial,  defined,  15,  82. 
Terrestrial,  defined,  88;  connected 
with  time,  38,  88;  from  maps,  87; 
from  observation,  88;  zero  merid- 
ian for,  88. 

Longitudes  of  places  mentioned  in 
the  text,  Appendix. 

Magnifying  power,  of  opera-glasses, 
67;  of  small  telescope,  81. 

Map,  of  Puppis,  33;  of  the  path  of 
Venus,  83. 

Maps,  geographical,  87;  lunar,  14,  55. 
See  also  star-maps. 

Mars,  appearance  in  small  telescope, 
84,  2;  change  in  brightness,  73, 
6;  conjunction  with  Venus,  60; 
located  among  the  stars,  59; 
motion  of,  83;  plotted  on  star- 
maps,  39,  Ex.  2. 

Mean  time,  see  Local  mean  time. 

Mean  sun,  22. 

Measuring  units,  for  distance  and 
angle,  33. 

Mercury  identified,  32,  51,  Exs.  1,  2. 


123 


INDEX 


Meridian,  celestial,  defined,  15, 8, 19, 

20. 

Meridian  line,  location  of,  6,  61. 
Meridian  stand,  7,  19. 
Meridian  stone  and  platform,  4. 
Milky    Way,    form,    position,    and 

motion,  76. 

Miscellaneous  appliances,  14. 
Moon,  almanac  data  for,  24,  25,  34; 

checks  for  altitude  and  azimuth, 

29,  51;  for  path  among  the  stars, 

57;    diurnal   path   charted,    80; 

times  of  phases,  65. 
Eclipse,  preparation  for  observing, 

70,  times  of  phases,  66. 
Observed,  with   opera-glasses,    55; 

with  small  telescope,  69,  70. 
Observed      without      magnifying 

power,  diurnal  path,  56,  80;  new 

moon,  45;  path  among  the  stars, 

57;   place   in   constellation,   46; 

rate    of    motion,    58;    sidereal 

period,  58;  synodic  period,  47. 
Moonlight  hours,  diagrams  for,  24. 
Motion,  apparent,  of  stars,  74;  of  sun, 

41,  63. 
Among  the  stars,  Daniel's  comet, 

72;  planets,  59,  83;  moon,  57. 
Rate    of,    for    comet,  72,  Obs.  2; 

for  moon,   58;  for  planets,   83, 

Obs.;  for  sun,  41,  63. 

Nadir,  defined,  15,  3. 

Nebulae,  with  opera-glasses,  77;  with 

small  telescope,  84,  5. 
Noon,  for  different  kinds  of  time,  22, 

49. 

See  also  Apparent  time. 
North  and  south  line,  6,  61. 
North  Star,  latitude  from,  78;  motion 

of  constellations  around,  2,  4- 
Time  of  southing,  mean,  64,  Ex.; 
standard,  38,  Ex.  4. 


Numerical  records,  17,  8,  9. 

Obliquity  of  ecliptic,  15,  28,  44,  Ex.  1, 
Observations,  fundamental,  2. 
Opera-glasses,  first  tests,  52;  field  of 

view,  67;  magnifying  power,  67. 
Used  in  observing,  sun,  moon,  and 

planets,   55,   70,   82;   stars   and 

nebulae,  77. 
Orientation  of  celestial  globe,  40. 

Parallels  of  declination,  defined,  15, 
16;  on  globe,  26;  on  star-maps,  21. 

Path,  apparent,  of  sun,  41. 
Among   the    stars,    observed    and 
plotted,   of  comet,   72,   Obs.   2; 
of  moon,  57;  of  planet,  83. 
Diurnal,  see  Diurnal  paths. 

Planets,    almanac    times    for    rising, 
southing,   conjunction,  etc.,   24, 
25,  34;  motion  of,  59,  83;  located 
on  globe,  51,  Exs.  1,  2,  59,  83; 
on  star-maps,  39,  Ex.  2. 
Observed   with   opera-glasses,    55; 
with  small  telescope,  84, 1,2,8,  4> 
Observed  without  magnifying  pow- 
er, color  and  brightness,  73,  1, 
4,  5,  6;  conjunction,  60;  identi- 
fication, 32,  51,  Exs.  1,  2;  path* 
among  the  stars,  83;  points  in 
diurnal  paths,  80;  position   near 
ecliptic,  75. 
See  also  individual  names. 

Plotting,  directions  for,  31,  39,  51; 
illustrations  of,  39,  41,  51,  57,  59, 
72,  80,  83. 

Plumb-line  booth,  described,  9;  used  for 
latitude,  43,  Obs;  2;  for  time,  62. 

Plumblines,  material,  8;  lighting,  8, 
62,  Obs.  2;  locating,  9. 

Polaris,  see  North  Star. 

Precession,  Corrections  for,  59,  72, 
Obs.  2. 


124 


INDEX 


Prime  vertical,  defined,  15,  9;  plumb 

lines  in,  9. 

Protractor,  described,  11;  used,  19,  43. 
Puppis  in  Argo-Navis  mapped,  33. 

Recording,  rules  for,  17,  33;  age  of 
moon,  55;  aperture  and  power  of 
telescope,  69. 

Refraction,  correction  for,  43,  Obs.  1. 

Right  ascension  and  declination, 
defined,  15,  23,  29;  given  in 
Ephemeris,  34;  in  astronomical 
journals,  50,  Ex.  3;  found  by 
interpolating,  50,  Exs.  2,  3;  read 
from  globe,  51,  59,  83;  from  star- 
maps,  21,  39. 

From  observation  and  plotting,  39, 
Ex.  2,  51,  Exs.  1,  4,  59,  72,  Obs. 
2,  83. 

Right  ascension  reduced  to  mean 
time,  64,  Ex. 

Right  ascension  of  meridian,  equal 
sidereal  time,  49;  used  in  orient- 
ing globe,  40. 

Rule,  for  checking  sun's  noon  altitude, 
28;  for  finding  latitude  from  sun's 
zenith  distance,  44;  for  standard 
time  kept  at  any  place,  23. 

Rules,  for  recording,  17;  for  passing 
from  one  kind  of  time  to  another, 
37,  38,  48. 

Saturn,  appearance  in  small  telescope, 
84,  4)  identification  in  sky,  32, 
Obs.;  setting  time  by  interpo- 
lating, 50,  Ex.  1. 

Shooting  stars,  71. 

Sidereal  day,  defined,  63;  length  of,  63. 

Sidereal  period  of  moon,  58. 

Sidereal  time,  defined,  49;  equal  right 
ascension  of  meridian,  49;  gam 
of,  on  mean  solar,  64;  reduced  to 
mean  time,  64,  Ex.;  effect  on 
orienting  globe,  40. 


From  star  transits,  62,  Obs.  2. 

Solstices,  defined,  15,  27. 

Observations  at,  sun's  noon  alti- 
tude, 43,  sun's  diurnal  path,  31, 80. 

Southing,  defined,  15,  21;  almanac 
times  of,  24,  25;  mean  time,  for 
Polaris,  64,  Ex.;  standard  time, 
38,  Ex.  4. 

Standard  meridians   established,   23. 

Standard  time,  defined,  22;  divisions 
of,  23;  changed,  to  local  mean, 
38;  to  Greenwich,  48;  globe  ori- 
ented for,  40;  noon  of,  22. 

Star-Atlas,  Proctor,  39,  Ex.  2. 

Star-catalogue,  34. 

Star-clusters,  with  opera-glasses,  77; 
with  small  telescopes,  84,  6. 

Star-line,  as  unit  of  measure,  33; 
evaluated  on  map  or  globe,  67; 
examples  of  use,  46,  59,  60,  72,  76. 

Star-maps,  described,  21;  compared 
with    globe,    26;    specially   pre- 
pared, 83. 
Used,  for  plotting,  39 ;  in  observing, 

see  Stars. 
See  also  Young's  Uranography. 

Stars,  almanac  data  for,  24,  25,  34; 
grouped  and  named,  21;  used  in 
testing  telescope,  68,  81. 
Observed,  with  opera-glasses,  77; 
with  altazimuth,  84,  6,  7,  8;  with 
transit  instrument,  86. 
Observed,  without  magnifying 
power,  for  color,  and  brightness, 
73,  2,  4,  7,  8,  9;  for  law  of  motion, 
74;  for  latitude,  78;  for  time,  62, 
Obs.  2;  for  length  of  sidereal  day, 
63;  in  fixing  sunset,  41;  in  ob- 
serving, comet,  72;  moon  46,  57; 
planets,  32,  59;  in  tracing  equa- 
tor and  ecliptic,  75. 
See  also  Double  stars,  Variable 
stars. 


125 


INDEX 


Sun,  almanac  data  for,  24,  25,  34; 
place,  marked  on  globe,  26;  used 
in  orienting  globe,  40. 
Checks,  for  altitude,  28;  for  alti- 
tude and  azimuth,  29;  for  diur- 
nal paths,  80. 
Eclipse,  82. 
Observed,  with  opera-glasses,  55; 

with  small  telescope,  69,  82. 
Observed       without      magnifying 
power,     apparent     motion     on 
sphere,  41,  63;  bright  image  under 
trees,  42,  82;  diurnal  paths,  18, 
30,  31;  for  latitude,  43,  44;  for 
time,    with    gnomon,    61;    with 
plumb  lines,  62;  with  sun-dial,  79. 
Sun-dial,  horizontal,  described,  13;  ad- 
justed and  read,  79. 
Sun  fast,  sun  slow,  36. 

See  also  equation  of  time. 
Sun  noon,  see  Apparent  noon. 
Synodic  period  of  moon,  47. 

Tables,  ABC,  described,  85. 

Constellations  in  groups,  20. 

Diurnal  paths,  19,  30,  80. 

Latitude   from  Polaris,   78. 

Longitude  of  Wide  View,  88. 

Positions  of  Mars  and  Jupiter,  59. 

Time-set,  Lawrence,  Kan.,  86. 
Telescope,  first  tests,  53;  field  of 
view,  68;  focal  length,  68;  light- 
gathering  power,  54;  magnifying 
power, ^81;  quality  of  object- 
ive, 81* 

Used    in    observing,    comet,    72; 
planets,  84,  1,  2,  3,  4;  stars,  84, 
86;  sun  and  moon,  69. 
Time,  kinds  of,  22,  49;  equation  of,  36. 


Reduction  of,  apparent  to  mean, 
37;  apparent  to  standard,  38, 
Ex.  5;  local  to  standard,  38; 
Greenwich  to  local  and  standard, 
48;  sidereal  to  mean,  64;  stand- 
ard to  Washington,  50,  Ex.  4. 

From  observation,  of  stars,  62, 
Obs.  2,  86;  of  sun,  at  noon,  62, 
Obs.  1;  of  sun's  image,  with 
gnomon,  61,  Obs.;  with  sun-dial, 
79. 

Longitude  determined  from,  88. 
Time  sections,  23. 

Transit  instrument,  home-made,  de- 
scribed, 10;  used  for  longitude, 
88;  for  time,  86,  88. 

Variable  stars,  Algol,  73,  8,  9. 

Method  of  observing,  73. 
Venus,  appearance  in  small  telescope, 
84,    1;   comparative    brightness, 
73,  5;  diurnal  path,  80;  distin- 
guished from  stars,  32;  greatest 
elongation,  83. 
Path  among  the  stars,  83. 
Vertical  circles,  denned,  15,  6,  7,  8,  9. 

Washington  time  from  standard,  50, 

Ex.  4. 
Works  of  reference,  14. 

Year,  length  of,  from  observation,  63. 

Young's  Uranography,  for  explain- 
ing star-maps,  21;  used  in  plot- 
ting, 39. 

Zenith,  denned,  15,  2;  declination  of, 
equal  latitude,  27;  located  on 
globe,  27. 

Zenith  distance,  defined,  15,  11; 
observed,  of  sun,  for  latitude,  43, 
44;  for  obliquity  of  ecliptic,  44. 


126 


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DEC  20 
DEC  20  t 


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REC'D  LD 


DEC  20  1943 


JUN  1  7  1963 


SEP    1     1944 


JAN  10  1947 





REC'D  L 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


